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Its value determines whether the chosen place-value digit stays the same or increases by 1."},{"text":"immediately to its left","correct":false,"explanation":"Looking left confuses the deciding digit with a higher place value. The deciding digit is immediately to the right of the digit being kept."},{"text":"two places to its right","correct":false,"explanation":"This skips over the actual deciding digit and can give the wrong result. You must inspect the digit immediately to the right of the chosen place."},{"text":"furthest to its right","correct":false,"explanation":"The final digit is not necessarily relevant to the chosen place value. Rounding is determined by the digit immediately to the right of the kept digit."}]},{"id":"f89d3e0e-f561-4d7f-b60b-0779a3e61179","cardType":"basic","points":1,"front":"If the deciding digit is 5, 6, 7, 8 or 9, what do you do?","back":"Round up: increase the kept digit by 1.","mcqOptions":[{"text":"Round up: increase the kept digit by 1.","correct":true,"explanation":"A deciding digit from 5 to 9 means the number is at or beyond the halfway point, so the kept digit must increase by 1."},{"text":"Round down: keep the kept digit the same.","correct":false,"explanation":"Keeping the digit unchanged applies when the deciding digit is from 0 to 4. For 5 to 9, round up by increasing the kept digit by 1."},{"text":"Round up: increase the deciding digit by 1.","correct":false,"explanation":"The deciding digit is discarded after it has been checked, so increasing it has no effect. Rounding up means increasing the kept digit by 1."},{"text":"Round down: decrease the kept digit by 1.","correct":false,"explanation":"Rounding down never means subtracting 1 from the kept digit. With a deciding digit from 5 to 9, increase the kept digit by 1."}]},{"id":"abae3a13-8617-4e3f-b9e5-92c477deea34","cardType":"basic","points":1,"front":"If the deciding digit is 0, 1, 2, 3 or 4, what do you do?","back":"Round down: keep the kept digit the same.","mcqOptions":[{"text":"Round down: keep the kept digit the same.","correct":true,"explanation":"A deciding digit from 0 to 4 lies below the halfway point. The kept digit therefore remains unchanged, while the digits after it are removed or replaced."},{"text":"Round up: increase the kept digit by 1.","correct":false,"explanation":"Increasing the kept digit is required only when the deciding digit is from 5 to 9. For 0 to 4, keep the kept digit unchanged."},{"text":"Round down: decrease the kept digit by 1.","correct":false,"explanation":"The phrase round down can misleadingly suggest subtraction, but the kept digit is not decreased. With a deciding digit from 0 to 4, it stays unchanged."},{"text":"Round down: replace the kept digit with 0.","correct":false,"explanation":"Zeros replace digits to the right when rounding whole numbers, not the kept digit itself. For a deciding digit from 0 to 4, the kept digit remains unchanged."}]},{"id":"92ef2ca3-de7c-4495-9a25-dcaa6568d2e2","cardType":"basic","points":1,"front":"When rounding a whole number, what replaces digits to the right?","back":"Zeros replace all digits to the right.","mcqOptions":[{"text":"Zeros replace all digits to the right.","correct":true,"explanation":"Zeros preserve the whole number’s place value after rounding. For example, rounding to the nearest hundred requires the tens and units digits to become zero."},{"text":"Nines replace all digits to the right.","correct":false,"explanation":"Using nines would increase the rounded number and would not preserve the intended place value. All whole-number digits to the right are replaced by zeros."},{"text":"Fives replace all digits to the right.","correct":false,"explanation":"The deciding digit may be compared with 5, but it is not used as a replacement. Digits to the right are replaced by zeros."},{"text":"Nothing replaces all digits to the right.","correct":false,"explanation":"Simply deleting the digits would change the number’s place value. When rounding a whole number, zeros must replace every digit to the right of the kept digit."}]},{"id":"97489b49-5bf9-4c31-8b7d-1fd73ec10af6","cardType":"basic","points":1,"front":"Round $468$ to the nearest hundred.","back":"$500$","mcqOptions":[{"text":"$500$","correct":true,"explanation":"The hundreds digit is 4 and the deciding tens digit is 6. Since 6 is at least 5, the hundreds digit increases to give $500$."},{"text":"$400$","correct":false,"explanation":"This treats the tens digit 6 as though it were below 5. Since 6 requires rounding up, $468$ rounds to $500$ to the nearest hundred."},{"text":"$470$","correct":false,"explanation":"This is the result of rounding to the nearest ten rather than the nearest hundred. Using the tens digit 6, the correct hundred is $500$."},{"text":"$460$","correct":false,"explanation":"This truncates the number at the tens place instead of rounding to the requested place. To the nearest hundred, the deciding digit 6 gives $500$."}]},{"id":"b1f72168-996f-4575-8b29-ce75bd2de7f5","cardType":"basic","points":1,"front":"Round $5274$ to the nearest thousand.","back":"$5000$","mcqOptions":[{"text":"$5000$","correct":true,"explanation":"The thousands digit is 5 and the deciding hundreds digit is 2. Since 2 is below 5, the thousands digit stays unchanged, giving $5000$."},{"text":"$6000$","correct":false,"explanation":"This rounds up merely because digits follow the thousands digit. The deciding hundreds digit is 2, which is below 5, so the answer is $5000$."},{"text":"$5300$","correct":false,"explanation":"This rounds $5274$ to the nearest hundred, not the nearest thousand. At the thousands place, the deciding hundreds digit is 2, giving $5000$."},{"text":"$5270$","correct":false,"explanation":"This rounds to the nearest ten by using the units digit. The question asks for the nearest thousand, so the hundreds digit 2 gives $5000$."}]},{"id":"8fdecaa9-cb18-49c0-a091-254213fd928f","cardType":"basic","points":1,"front":"Round $7518$ to the nearest hundred.","back":"$7500$","mcqOptions":[{"text":"$7500$","correct":true,"explanation":"The hundreds digit is 5 and the deciding tens digit is 1. Since 1 is below 5, the hundreds digit stays unchanged, giving $7500$."},{"text":"$7600$","correct":false,"explanation":"This incorrectly uses the hundreds digit 5 to decide the rounding. For the nearest hundred, inspect the tens digit 1, so the answer is $7500$."},{"text":"$7520$","correct":false,"explanation":"This is the result of rounding to the nearest ten rather than the nearest hundred. The deciding tens digit is 1, so the correct answer is $7500$."},{"text":"$7000$","correct":false,"explanation":"This rounds to the nearest thousand rather than the nearest hundred. For hundreds, the tens digit 1 means the number rounds to $7500$."}]},{"id":"7eaab5ed-de8f-4df4-beee-cf133ada70ad","cardType":"cloze","points":null,"front":"The halfway point between 300 and 400 is [ ], so 376 rounds to [ ] to the nearest hundred.","back":"The halfway point between 300 and 400 is 350, so 376 rounds to 400 to the nearest hundred.","mcqOptions":[{"text":"The halfway point between 300 and 400 is 350, so 376 rounds to 400 to the nearest hundred.","correct":true,"explanation":"The midpoint is $350$. Since $376$ is above this halfway point and closer to $400$ than to $300$, it rounds to $400$."},{"text":"The halfway point between 300 and 400 is 350, so 376 rounds to 300 to the nearest hundred.","correct":false,"explanation":"Although the halfway point is correctly identified as $350$, the rounding direction is reversed. Since $376$ is above $350$, it rounds up to $400$."},{"text":"The halfway point between 300 and 400 is 400, so 376 rounds to 400 to the nearest hundred.","correct":false,"explanation":"The rounding result is right, but $400$ is an endpoint rather than the midpoint. Halfway between $300$ and $400$ is $350$, and $376$ rounds to $400$."},{"text":"The halfway point between 300 and 400 is 300, so 376 rounds to 300 to the nearest hundred.","correct":false,"explanation":"This mistakes an endpoint for the halfway point and then rounds in the wrong direction. The midpoint is $350$, and because $376$ exceeds it, the answer is $400$."}]},{"id":"e34a5919-4e65-484a-aaef-bd261f6cf2a5","cardType":"basic","points":1,"front":"In $3.847$, which digit is the 2nd decimal place?","back":"4","mcqOptions":[{"text":"4","correct":true,"explanation":"The first digit after the decimal point is 8, so the second digit is 4. Therefore, 4 occupies the hundredths place."},{"text":"8","correct":false,"explanation":"The digit 8 is the first digit after the decimal point, so it is in the tenths place. The second decimal place is occupied by 4."},{"text":"7","correct":false,"explanation":"The digit 7 is the third digit after the decimal point, which is the thousandths place. The second decimal place contains 4."},{"text":"3","correct":false,"explanation":"The digit 3 is before the decimal point, so it is in the units place. Counting after the decimal point, the second digit is 4."}]},{"id":"bf112cb7-51d4-477a-8748-c0ed6923c830","cardType":"cloze","points":null,"front":"The 1st decimal place is [ ]; the 2nd decimal place is [ ].","back":"The 1st decimal place is tenths; the 2nd decimal place is hundredths.","mcqOptions":[{"text":"The 1st decimal place is tenths; the 2nd decimal place is hundredths.","correct":true,"explanation":"Decimal place values decrease by powers of ten: the first digit after the point represents tenths, and the second represents hundredths."},{"text":"The 1st decimal place is hundredths; the 2nd decimal place is tenths.","correct":false,"explanation":"This reverses the order of the first two decimal places. Moving right from the decimal point gives tenths first and then hundredths."},{"text":"The 1st decimal place is units; the 2nd decimal place is hundredths.","correct":false,"explanation":"Units are immediately before the decimal point, not after it. The first decimal place is tenths, while the second decimal place is hundredths."},{"text":"The 1st decimal place is tenths; the 2nd decimal place is thousandths.","correct":false,"explanation":"Thousandths are the third decimal place, not the second. The sequence after the decimal point is tenths, hundredths, then thousandths."}]},{"id":"9d9b6aff-8e26-4181-a5ed-f4729a9dd872","cardType":"basic","points":1,"front":"What must an answer correct to 3 decimal places show?","back":"Exactly 3 digits after the decimal point.","mcqOptions":[{"text":"Exactly 3 digits after the decimal point.","correct":true,"explanation":"Decimal places count the number of digits written after the decimal point. An answer correct to 3 decimal places must therefore display exactly three such digits."},{"text":"Exactly 2 digits after the decimal point.","correct":false,"explanation":"Showing two digits would give an answer to 2 decimal places. An answer to 3 decimal places must display exactly three digits after the decimal point."},{"text":"Exactly 4 digits after the decimal point.","correct":false,"explanation":"Showing four digits would give an answer to 4 decimal places. For 3 decimal places, exactly three digits must appear after the decimal point."},{"text":"At most 3 digits after the decimal point.","correct":false,"explanation":"The phrase “at most” wrongly allows fewer than three digits. A stated accuracy of 3 decimal places requires exactly three digits, including any necessary trailing zeros."}]},{"id":"88289f16-22ce-4d19-9b89-c1d0930bbb01","cardType":"basic","points":1,"front":"Round $2.83$ to 1 decimal place.","back":"$2.8$","mcqOptions":[{"text":"$2.8$","correct":true,"explanation":"The tenths digit is 8 and the next digit is 3. Since 3 is less than 5, the tenths digit stays unchanged."},{"text":"$2.9$","correct":false,"explanation":"This rounds up despite the hundredths digit being 3. Only a next digit of 5 or more would increase the tenths digit, so the answer is $2.8$."},{"text":"$3.0$","correct":false,"explanation":"This effectively rounds to the nearest whole number rather than to 1 decimal place. Keeping the tenths digit and checking the 3 gives $2.8$."},{"text":"$2.3$","correct":false,"explanation":"This mistakes the hundredths digit for the required tenths digit. The first digit after the decimal point is 8, and the following 3 leaves it unchanged."}]},{"id":"f236fb16-51c4-409c-b469-0324c0f47166","cardType":"basic","points":1,"front":"Round $23.1681$ to 2 decimal places.","back":"$23.17$","mcqOptions":[{"text":"$23.17$","correct":true,"explanation":"Keep the hundredths digit, 6, and inspect the next digit, 8. Since 8 is at least 5, the 6 rounds up to 7."},{"text":"$23.16$","correct":false,"explanation":"This truncates the number instead of rounding it. The third decimal digit is 8, so the hundredths digit must increase from 6 to 7, giving $23.17$."},{"text":"$23.18$","correct":false,"explanation":"This keeps the third decimal digit rather than using it only as a rounding indicator. The 8 increases the hundredths digit from 6 to 7, giving $23.17$."},{"text":"$23.20$","correct":false,"explanation":"This rounds the number to 1 decimal place and then adds a zero. For 2 decimal places, retain 16 and use the following 8 to obtain $23.17$."}]},{"id":"e28db508-a64a-4d84-acc6-f2ee46c4dcac","cardType":"basic","points":1,"front":"Round $5.4096$ to 3 decimal places.","back":"$5.410$","mcqOptions":[{"text":"$5.410$","correct":true,"explanation":"The first three decimal digits are 409, and the next digit is 6, so 409 rounds up to 410. The final zero is retained to show 3 decimal places."},{"text":"$5.409$","correct":false,"explanation":"This simply cuts off the fourth decimal digit. Because that digit is 6, the thousandths digit must round up, carrying through 9 and producing $5.410$."},{"text":"$5.400$","correct":false,"explanation":"This rounds to 2 decimal places before padding with a zero. At 3 decimal places, 409 is retained first and the following 6 rounds it to 410."},{"text":"$5.500$","correct":false,"explanation":"This rounds to 1 decimal place before adding two zeros. The question requires three decimal places, so the fourth decimal digit rounds 409 to 410."}]},{"id":"c2139b8d-1c7b-45b1-a086-10fa187eeba0","cardType":"basic","points":2,"front":"Why must $5.410$ keep the final zero for 3 decimal places?","back":"It shows exactly 3 digits after the decimal point.","mcqOptions":[{"text":"It shows exactly 3 digits after the decimal point.","correct":true,"explanation":"A trailing zero does not change the numerical value, but it records the required accuracy. Writing $5.410$ makes clear that the result is given to 3 decimal places."},{"text":"It shows exactly 3 significant figures in the number.","correct":false,"explanation":"The number $5.410$ actually has four significant figures because its final zero follows non-zero digits. The zero is needed to show exactly three decimal places."},{"text":"It shows exactly 3 digits before the decimal point.","correct":false,"explanation":"There is only one digit before the decimal point in $5.410$. The retained zero instead ensures that exactly three digits appear after the decimal point."},{"text":"It makes $5.410$ greater than $5.41$.","correct":false,"explanation":"Trailing zeros after a decimal do not change a number’s value, so $5.410$ and $5.41$ are equal. The zero communicates accuracy to 3 decimal places."}]},{"id":"eff63ae3-5485-4ba9-b6d6-35cbad1aec6b","cardType":"cloze","points":null,"front":"Significant figures are counted from the first [ ] digit; zeros before it are [ ].","back":"Significant figures are counted from the first non-zero digit; zeros before it are not significant.","mcqOptions":[{"text":"Significant figures are counted from the first non-zero digit; zeros before it are not significant.","correct":true,"explanation":"Leading zeros only locate the decimal point and do not indicate measured precision. Counting significant figures begins with the first digit from 1 to 9."},{"text":"Significant figures are counted from the first zero digit; zeros before it are significant.","correct":false,"explanation":"This incorrectly counts leading zeros as measured digits. Significant figures begin at the first non-zero digit, and any zeros before it are not significant."},{"text":"Significant figures are counted from the first non-zero digit; zeros before it are significant.","correct":false,"explanation":"Although counting starts at the first non-zero digit, the statement then wrongly includes earlier zeros. Those leading zeros only set place value and are not significant."},{"text":"Significant figures are counted from the first decimal digit; zeros before it are not significant.","correct":false,"explanation":"Significant figures do not necessarily begin after the decimal point; whole-number digits may be significant too. Counting starts at the first non-zero digit."}]},{"id":"46337e29-9fd8-4d4e-aa22-4fcaa34bebc4","cardType":"basic","points":1,"front":"In $0.00681$, which digit is the first significant figure?","back":"6","mcqOptions":[{"text":"6","correct":true,"explanation":"Leading zeros are not significant, so the first non-zero digit is 6. It is therefore the first significant figure in $0.00681$."},{"text":"0","correct":false,"explanation":"The zeros before 6 only locate the decimal value and are not significant. The first non-zero digit, 6, is the first significant figure."},{"text":"8","correct":false,"explanation":"The digit 8 is the second significant figure because 6 has already appeared. The first significant figure in the number is 6."},{"text":"1","correct":false,"explanation":"The digit 1 is the third significant figure, not the first. Ignoring the leading zeros, the significant digits begin with 6."}]},{"id":"df83da8a-0b8d-4624-98a8-e4a22e43ada6","cardType":"basic","points":2,"front":"Why does the 0 in $90437$ count as a significant figure?","back":"It comes after the first non-zero digit.","mcqOptions":[{"text":"It comes after the first non-zero digit.","correct":true,"explanation":"Once the first non-zero digit has appeared, every following digit is significant, including zeros. Since 0 follows 9, it counts as significant."},{"text":"It comes before the first non-zero digit.","correct":false,"explanation":"Zeros before the first non-zero digit are leading zeros and do not count as significant. Here, the 0 follows 9, so it is significant."},{"text":"It is the final digit in the number.","correct":false,"explanation":"The 0 is not the final digit, and being final would not automatically make a whole-number zero significant. It counts because it follows the first non-zero digit."},{"text":"It appears to the right of a decimal point.","correct":false,"explanation":"There is no decimal point in $90437$, so this cannot explain the zero’s significance. The zero counts because it occurs after the first non-zero digit."}]},{"id":"2980bcc6-2040-4d6d-94e0-7ab90942114c","cardType":"basic","points":1,"front":"Round $58.165$ to 1 significant figure.","back":"$60$","mcqOptions":[{"text":"$60$","correct":true,"explanation":"The first significant digit is 5 and the next digit is 8, so 5 rounds up to 6. Its place value is tens, giving $60$."},{"text":"$50$","correct":false,"explanation":"Keeping 5 unchanged ignores the following digit 8. Since 8 is at least 5, the tens digit rounds up, giving the correct answer $60$."},{"text":"$58$","correct":false,"explanation":"This confuses one significant figure with rounding to the nearest whole number. For $58.165$, one significant figure means rounding to the nearest ten, giving $60$."},{"text":"$100$","correct":false,"explanation":"A two-digit number rounds to the nearest ten when one significant figure is required, not the nearest hundred. Since 58 is nearer 60, the answer is $60$."}]},{"id":"4e63a5bb-6e22-4b87-90c3-6522d6c7d876","cardType":"basic","points":1,"front":"Round $0.06849$ to 2 significant figures.","back":"$0.068$","mcqOptions":[{"text":"$0.068$","correct":true,"explanation":"The first two significant digits are 6 and 8. The following digit is 4, so the 8 remains unchanged and the result is $0.068$."},{"text":"$0.069$","correct":false,"explanation":"The digit immediately after the first two significant figures is 4, so rounding up is not required. Later digits do not make the 4 round up; the answer is $0.068$."},{"text":"$0.0685$","correct":false,"explanation":"This result has three significant figures rather than two. Keeping only 6 and 8, then checking the following 4, gives the correct result $0.068$."},{"text":"$0.07$","correct":false,"explanation":"This gives only one significant figure because the trailing zero has not been shown. To two significant figures, 6 and 8 must be retained, giving $0.068$."}]},{"id":"657577cc-06d7-4d63-92b7-f7bfef624742","cardType":"basic","points":1,"front":"Round $90437$ to 2 significant figures.","back":"$90000$","mcqOptions":[{"text":"$90000$","correct":true,"explanation":"The first two significant digits are 9 and 0 because the zero follows a non-zero digit. The next digit is 4, so the result stays $90000$."},{"text":"$94000$","correct":false,"explanation":"This incorrectly ignores the zero between 9 and 4. That zero is significant, so the first two significant figures are 9 and 0, giving $90000$."},{"text":"$90400$","correct":false,"explanation":"This keeps three significant figures: 9, 0 and 4. Rounding to two significant figures requires checking the 4 and replacing it and later digits with zeros, giving $90000$."},{"text":"$91000$","correct":false,"explanation":"This rounds the second significant digit up even though the following digit is 4. Since 4 is below 5, the zero stays unchanged and the answer is $90000$."}]},{"id":"cdad4225-3ead-44a6-b178-da1bc6506c5b","cardType":"cloze","points":null,"front":"The phrase “correct to” means [ ] that level of [ ].","back":"The phrase “correct to” means round to that level of accuracy.","mcqOptions":[{"text":"The phrase “correct to” means round to that level of accuracy.","correct":true,"explanation":"In rounding questions, “correct to” instructs you to round a value to the stated degree of accuracy, such as a given number of decimal places or significant figures."},{"text":"The phrase “correct to” means round up that level of accuracy.","correct":false,"explanation":"“Correct to” does not mean always increasing the value; rounding may increase or decrease it. It means to round to the specified level of accuracy."},{"text":"The phrase “correct to” means round to that level of error.","correct":false,"explanation":"The stated level describes the accuracy required, not the amount of error to introduce. “Correct to” means to round to that level of accuracy."},{"text":"The phrase “correct to” means truncate to that level of uncertainty.","correct":false,"explanation":"Truncation simply removes later digits and is not the same as rounding, while uncertainty describes a range rather than the requested accuracy. The phrase means to round to that level of accuracy."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Rounding","title":"Rounding Flashcards","topbar":{"backHref":"/igcse/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"24f443e9-ab22-43e8-98e6-073be5e73953","walled":"$L39"}],"$L3a","$L3b"]