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24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/gcse/maths/ocr/grade-1-1-7-rounding/flashcards","label":"Rounding","subjectCode":"gcse_maths__ocr","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"fb8cd41b-9f18-9c9b-919d-388b508444fa","title":"Rounding Flashcards","topicId":"d3456a36-bccf-469d-86d2-cc4cb2dba6e0","topicSlug":"grade-1-1-7-rounding","cards":[{"id":"501661dc-f34f-9994-fc5b-6ae1d0015e84","cardType":"basic","points":1,"front":"If the digit to the right is 0, 1, 2, 3, or 4, what happens?","back":"Round down.","mcqOptions":[{"text":"Round down.","correct":true,"explanation":"A following digit from 0 to 4 is below the halfway point, so the rounding digit stays the same and the number rounds down."},{"text":"Round up.","correct":false,"explanation":"Rounding up for digits below 5 reverses the standard rule. A following digit from 0 to 4 means the number should round down."},{"text":"Round to 5.","correct":false,"explanation":"Five is the threshold for choosing a direction, not a value to which every number is rounded. Digits from 0 to 4 require rounding down."},{"text":"Round to an even digit.","correct":false,"explanation":"Rounding to an even digit is associated with a different tie-breaking convention, not ordinary GCSE rounding. A following digit below 5 means round down."}]},{"id":"92713610-c34b-792a-9596-6ac77f4f9e89","cardType":"basic","points":1,"front":"If the digit to the right is 5, 6, 7, 8, or 9, what happens?","back":"Round up.","mcqOptions":[{"text":"Round up.","correct":true,"explanation":"A following digit from 5 to 9 reaches or exceeds the halfway point, so the rounding digit increases by one and the number rounds up."},{"text":"Round down.","correct":false,"explanation":"Rounding down for digits of 5 or more reverses the standard rule. A following digit from 5 to 9 means the number should round up."},{"text":"Round to 5.","correct":false,"explanation":"Five is the threshold that determines the rounding direction, not the final digit required. Any following digit from 5 to 9 means round up."},{"text":"Round to an odd digit.","correct":false,"explanation":"Ordinary rounding does not choose an odd final digit. The deciding factor is whether the following digit is at least 5, in which case you round up."}]},{"id":"ad39075a-ca52-a0a1-0711-7f69770a50f6","cardType":"cloze","points":null,"front":"For the nearest hundred, look at the [ ] digit.","back":"For the nearest hundred, look at the tens digit.","mcqOptions":[{"text":"tens","correct":true,"explanation":"The tens digit is immediately to the right of the hundreds digit, so it determines whether the hundreds digit rounds up or down."},{"text":"hundreds","correct":false,"explanation":"The hundreds digit is the place being rounded, not the deciding digit. For the nearest hundred, inspect the tens digit immediately to its right."},{"text":"units","correct":false,"explanation":"The units digit is too far to the right to decide rounding to the nearest hundred. The tens digit determines the correct direction."},{"text":"thousands","correct":false,"explanation":"The thousands digit lies to the left of the hundreds place and is not the deciding digit. For the nearest hundred, look at the tens digit."}]},{"id":"2383c7d0-82a6-2bdf-63a7-2386e2402116","cardType":"basic","points":1,"front":"Round 376 to the nearest hundred.","back":"400","mcqOptions":[{"text":"400","correct":true,"explanation":"The tens digit of 376 is 7, so the hundreds digit rounds up from 3 to 4. Therefore, 376 rounds to 400."},{"text":"300","correct":false,"explanation":"Rounding to 300 incorrectly ignores that the tens digit is 7. Since 7 is at least 5, the hundreds digit must round up to give 400."},{"text":"380","correct":false,"explanation":"This is 376 rounded to the nearest ten rather than the nearest hundred. For hundreds, the tens digit 7 makes the answer 400."},{"text":"370","correct":false,"explanation":"This truncates the number to a multiple of ten instead of rounding to a multiple of one hundred. The correct rounded value is 400."}]},{"id":"9600f34b-ba9f-502f-838b-645fc6fbee82","cardType":"basic","points":1,"front":"Round 7642 to the nearest hundred.","back":"7600","mcqOptions":[{"text":"7600","correct":true,"explanation":"The tens digit of 7642 is 4, which is below 5, so the hundreds digit remains 6. The rounded number is 7600."},{"text":"7700","correct":false,"explanation":"This rounds the hundreds digit up despite the tens digit being only 4. Since 4 is below 5, 7642 rounds down to 7600."},{"text":"7640","correct":false,"explanation":"This is 7642 rounded to the nearest ten, using the units digit. Rounding to the nearest hundred requires the answer 7600."},{"text":"7000","correct":false,"explanation":"This uses the nearest thousand instead of the nearest hundred. Looking at the tens digit 4 shows that 7642 rounds to 7600."}]},{"id":"91e46d15-ae41-eb9e-3347-0f1d57581989","cardType":"basic","points":1,"front":"Round 2491 to the nearest hundred.","back":"2500","mcqOptions":[{"text":"2500","correct":true,"explanation":"The tens digit of 2491 is 9, so the hundreds digit increases from 4 to 5. Thus, 2491 rounds to 2500."},{"text":"2400","correct":false,"explanation":"This rounds down despite the tens digit being 9. Since 9 is at least 5, the hundreds digit must increase, giving 2500."},{"text":"2490","correct":false,"explanation":"This is the result of rounding 2491 to the nearest ten rather than the nearest hundred. To the nearest hundred, it is 2500."},{"text":"2000","correct":false,"explanation":"This rounds to the nearest thousand, which is the wrong place value. Using the tens digit to round to hundreds gives 2500."}]},{"id":"58fa6238-8bf5-9764-0a85-b71d026178d2","cardType":"cloze","points":null,"front":"A number rounded to the nearest hundred should end in [ ].","back":"A number rounded to the nearest hundred should end in two zeros.","mcqOptions":[{"text":"two zeros","correct":true,"explanation":"Every multiple of one hundred has zeros in both the tens and units places, so a number rounded to the nearest hundred ends in two zeros."},{"text":"one zero","correct":false,"explanation":"Ending in only one zero identifies a multiple of ten, not necessarily a multiple of one hundred. Nearest-hundred answers must end in two zeros."},{"text":"three zeros","correct":false,"explanation":"Three zeros indicate a multiple of one thousand, which is more restrictive than required. A number rounded to the nearest hundred ends in two zeros."},{"text":"two nines","correct":false,"explanation":"Nines do not mark multiples of one hundred. Rounding to the nearest hundred makes both the tens and units digits zero, producing two ending zeros."}]},{"id":"751f6a83-495d-59d0-609c-97874a6d0f1a","cardType":"cloze","points":null,"front":"For the nearest thousand, look at the [ ] digit.","back":"For the nearest thousand, look at the hundreds digit.","mcqOptions":[{"text":"hundreds","correct":true,"explanation":"The hundreds digit is immediately to the right of the thousands digit, so it determines whether the thousands digit rounds up or down."},{"text":"thousands","correct":false,"explanation":"The thousands digit is the place being rounded, not the deciding digit. To round to the nearest thousand, inspect the hundreds digit."},{"text":"tens","correct":false,"explanation":"The tens digit is too far to the right to determine rounding to the nearest thousand. The hundreds digit provides the required comparison with 5."},{"text":"ten-thousands","correct":false,"explanation":"The ten-thousands digit lies to the left of the place being rounded. The deciding digit for the nearest thousand is the hundreds digit."}]},{"id":"521dbccf-d10f-3b4f-27ff-00cd6c337e8e","cardType":"basic","points":1,"front":"Round 4863 to the nearest thousand.","back":"5000","mcqOptions":[{"text":"5000","correct":true,"explanation":"The hundreds digit is 8, which is at least 5, so the thousands digit rounds up from 4 to 5."},{"text":"4000","correct":false,"explanation":"This rounds down despite the hundreds digit being 8. Since 4863 is above 4500, it rounds up to 5000."},{"text":"4800","correct":false,"explanation":"This gives a value rounded to the nearest hundred, not the nearest thousand. To the nearest thousand, 4863 rounds to 5000."},{"text":"4900","correct":false,"explanation":"This incorrectly rounds to the nearest hundred. For the nearest thousand, the hundreds digit is checked, so 4863 rounds to 5000."}]},{"id":"5ded6dac-fcc8-44ef-1b14-5639151c5827","cardType":"basic","points":1,"front":"Round 9732 to the nearest thousand.","back":"10000","mcqOptions":[{"text":"10000","correct":true,"explanation":"The hundreds digit is 7, so the thousands digit rounds up. Increasing 9 thousands by one produces 10000."},{"text":"9000","correct":false,"explanation":"This rounds down even though the hundreds digit is 7. Since 9732 is at least 9500, it rounds up to 10000."},{"text":"9700","correct":false,"explanation":"This rounds to the nearest hundred rather than the nearest thousand. Checking the hundreds digit shows that 9732 rounds to 10000."},{"text":"11000","correct":false,"explanation":"This increases the thousands value too far. Rounding 9732 up adds one thousand to 9000, giving 10000, not 11000."}]},{"id":"fd5ad5d9-b637-895d-4504-8dd61290771c","cardType":"basic","points":1,"front":"When rounding to the nearest thousand, which digits become zeros?","back":"Hundreds, tens and units.","mcqOptions":[{"text":"Hundreds, tens and units.","correct":true,"explanation":"When rounding to the nearest thousand, every place value to the right of the thousands digit is replaced by zero."},{"text":"Tens and units.","correct":false,"explanation":"This describes the digits replaced when rounding to the nearest hundred. For the nearest thousand, the hundreds, tens and units digits all become zeros."},{"text":"Thousands, hundreds and tens.","correct":false,"explanation":"The thousands digit is retained or increased, rather than changed to zero. The hundreds, tens and units digits become zeros."},{"text":"Hundreds and tens.","correct":false,"explanation":"This misses the units digit, which must also become zero. Rounding to the nearest thousand replaces the hundreds, tens and units digits."}]},{"id":"98b702eb-6d6e-2ee1-64ad-92fd5f19604c","cardType":"cloze","points":null,"front":"The first decimal place is [ ] and the second is [ ].","back":"The first decimal place is tenths and the second is hundredths.","mcqOptions":[{"text":"The first decimal place is tenths and the second is hundredths.","correct":true,"explanation":"Place values immediately after the decimal point decrease by powers of ten: the first is tenths and the second is hundredths."},{"text":"The first decimal place is hundredths and the second is thousandths.","correct":false,"explanation":"This starts counting one position too far to the right. The first decimal place is tenths and the second is hundredths."},{"text":"The first decimal place is units and the second is tenths.","correct":false,"explanation":"Units are immediately before the decimal point, not after it. The first two decimal places are tenths and hundredths."},{"text":"The first decimal place is tenths and the second is thousandths.","correct":false,"explanation":"This skips the hundredths place between tenths and thousandths. The second decimal place is hundredths, while thousandths is third."}]},{"id":"0dfbe37b-d64c-bc96-2d0a-d69c3039b4a6","cardType":"basic","points":1,"front":"Round 8.36 to 1 decimal place.","back":"8.4","mcqOptions":[{"text":"8.4","correct":true,"explanation":"The tenths digit is 3 and the following hundredths digit is 6, so the tenths digit rounds up to 4."},{"text":"8.3","correct":false,"explanation":"This truncates the number instead of rounding it. The following digit is 6, so the tenths digit rounds up and gives 8.4."},{"text":"8.36","correct":false,"explanation":"This leaves two decimal places unchanged. Rounding to one decimal place requires checking the 6, which makes the result 8.4."},{"text":"8.37","correct":false,"explanation":"This incorrectly rounds the hundredths digit and still keeps two decimal places. To one decimal place, the correct result is 8.4."}]},{"id":"f6a4688b-9600-5d1f-cff0-c4034e6d1ef5","cardType":"basic","points":2,"front":"Why is 8.36 to 1 decimal place not 8.3?","back":"The hundredths digit is 6, so 3 rounds up.","mcqOptions":[{"text":"The hundredths digit is 6, so 3 rounds up.","correct":true,"explanation":"To round to one decimal place, inspect the hundredths digit. Since it is 6, the retained tenths digit increases from 3 to 4."},{"text":"The hundredths digit is 3, so 6 rounds up.","correct":false,"explanation":"This reverses the place values: 3 is the tenths digit and 6 is the hundredths digit. The 6 makes 3 round up."},{"text":"The hundredths digit is 6, so 3 rounds down.","correct":false,"explanation":"A following digit of 6 causes rounding up, not down. Therefore the tenths digit increases from 3 to 4, giving 8.4."},{"text":"The thousandths digit is 6, so 3 rounds up.","correct":false,"explanation":"The 6 is in the hundredths place, not the thousandths place. It is the deciding digit and makes the tenths digit round up."}]},{"id":"90ab50a7-5442-3a50-e084-03e4b01d1d5e","cardType":"basic","points":1,"front":"Round 4.72851 to 3 decimal places.","back":"4.729","mcqOptions":[{"text":"4.729","correct":true,"explanation":"The third decimal digit is 8 and the next digit is 5, so 8 rounds up to 9, producing 4.729."},{"text":"4.728","correct":false,"explanation":"This truncates after three decimal places and ignores the following 5. That 5 makes the third decimal digit round up, giving 4.729."},{"text":"4.730","correct":false,"explanation":"This rounds the final digits too far and incorrectly creates a carry into the hundredths place. Only 8 increases to 9, giving 4.729."},{"text":"4.7285","correct":false,"explanation":"This leaves four decimal places rather than three. Using the next digit, 5, to round the third decimal place gives 4.729."}]},{"id":"5faeeff5-dc42-de23-3628-d7ed0e9d2acc","cardType":"cloze","points":null,"front":"When rounding to decimal places, start counting [ ].","back":"When rounding to decimal places, start counting after the decimal point.","mcqOptions":[{"text":"after the decimal point","correct":true,"explanation":"Decimal places are the positions to the right of the decimal point, beginning with tenths, followed by hundredths and thousandths."},{"text":"before the decimal point","correct":false,"explanation":"Positions before the decimal point are whole-number place values such as units and tens. Decimal places are counted after the decimal point."},{"text":"from the leftmost digit","correct":false,"explanation":"Starting at the leftmost digit counts significant figures rather than decimal places. For decimal places, counting begins after the decimal point."},{"text":"at the decimal point","correct":false,"explanation":"The decimal point separates place values but is not itself a decimal place. Counting starts after the decimal point, with the tenths digit."}]},{"id":"d35212f6-485b-8b6e-22d4-724aa0c0254f","cardType":"cloze","points":null,"front":"Significant figures start from the first [ ] digit.","back":"Significant figures start from the first non-zero digit.","mcqOptions":[{"text":"non-zero","correct":true,"explanation":"Leading zeros only locate the decimal point and do not count as significant figures. Therefore, counting begins at the first digit that is not zero."},{"text":"zero","correct":false,"explanation":"Leading zeros are placeholders rather than significant figures. The correct term is non-zero because significant figures begin at the first digit with a non-zero value."},{"text":"decimal","correct":false,"explanation":"The decimal point does not determine where significant figures begin. Counting starts from the first non-zero digit, whether it occurs before or after the decimal point."},{"text":"final","correct":false,"explanation":"Significant figures are counted from the beginning of the meaningful digits, not backwards from the final digit. The correct term is non-zero."}]},{"id":"ce1e41b5-4782-6822-b163-fe055868a489","cardType":"basic","points":1,"front":"In 0.4726, what is the first significant figure?","back":"4","mcqOptions":[{"text":"4","correct":true,"explanation":"The zero before the decimal point is a leading zero, so it is not significant. The first non-zero digit is 4, making it the first significant figure."},{"text":"0","correct":false,"explanation":"The zero before the decimal point only shows the number is less than one and is not significant. The first significant figure is therefore 4."},{"text":"7","correct":false,"explanation":"The digit 7 is the second significant figure because counting begins with the first non-zero digit. In 0.4726, the first significant figure is 4."},{"text":"2","correct":false,"explanation":"The digit 2 is the third significant figure, not the first. Ignoring the leading zero, the significant digits begin 4, 7, 2, 6."}]},{"id":"ee9e493f-9215-7465-2a36-e7b3bdad3569","cardType":"basic","points":1,"front":"Round 64.82 to 1 significant figure.","back":"60","mcqOptions":[{"text":"60","correct":true,"explanation":"The first significant digit is 6 in the tens column. The next digit is 4, so 6 stays unchanged and the units become zero."},{"text":"70","correct":false,"explanation":"Rounding to 70 would require the next digit to be 5 or greater. Here it is 4, so 64.82 rounds down to 60."},{"text":"65","correct":false,"explanation":"This rounds to the nearest whole number rather than to one significant figure. One significant figure keeps the tens digit, giving 60."},{"text":"64.8","correct":false,"explanation":"This value is rounded to three significant figures because 6, 4 and 8 remain. Keeping only the first significant digit gives 60."}]},{"id":"6a4402e4-1264-3360-d880-ba738e8fb6e2","cardType":"basic","points":1,"front":"Round 0.5837 to 2 significant figures.","back":"0.58","mcqOptions":[{"text":"0.58","correct":true,"explanation":"The first two significant digits are 5 and 8. The following digit is 3, so the 8 remains unchanged and the result is 0.58."},{"text":"0.59","correct":false,"explanation":"This incorrectly rounds the second significant digit up even though the following digit is 3. Since 3 is below 5, the correct result is 0.58."},{"text":"0.6","correct":false,"explanation":"This keeps only one significant figure, rounding the 5 up because the next digit is 8. Two significant figures must be retained, giving 0.58."},{"text":"0.584","correct":false,"explanation":"This is rounded to three significant figures, retaining 5, 8 and 4 after rounding. At two significant figures, the correct result is 0.58."}]},{"id":"bafebdad-72db-d563-f150-52c335c92a47","cardType":"basic","points":1,"front":"Round 68542 to 2 significant figures.","back":"69000","mcqOptions":[{"text":"69000","correct":true,"explanation":"The first two significant digits are 6 and 8. The following digit is 5, so 68 rounds up to 69, with zeros preserving place value."},{"text":"68000","correct":false,"explanation":"This truncates the number after two significant digits and ignores the following 5. Since that digit requires rounding up, the correct result is 69000."},{"text":"6900","correct":false,"explanation":"The significant digits have been rounded correctly, but one placeholder zero is missing, changing the number’s size. The correct place value gives 69000."},{"text":"70000","correct":false,"explanation":"This is the result of rounding to one significant figure, where 6 rounds up to 7. Keeping two significant figures instead gives 69000."}]},{"id":"23a39bb2-ddbe-ccd9-0542-a30ac1d9e731","cardType":"basic","points":2,"front":"Why is 69000 not written as 69 after rounding a large whole number?","back":"The zeros show the size of the number.","mcqOptions":[{"text":"The zeros show the size of the number.","correct":true,"explanation":"The zeros preserve the place value of 69 after rounding, showing that the result represents sixty-nine thousand rather than sixty-nine."},{"text":"The zeros show the number of decimal places.","correct":false,"explanation":"These zeros are in a whole number and do not indicate decimal places. They preserve place value, so their purpose is to show the size of the number."},{"text":"The zeros show the number of significant figures.","correct":false,"explanation":"Placeholder zeros in 69000 do not necessarily count as significant figures without extra notation. They are needed to show the number’s size and place value."},{"text":"The zeros show the exactness of the answer.","correct":false,"explanation":"Rounding makes the result an approximation, so the zeros do not prove exactness. They preserve the thousands place and therefore show the size of the number."}]},{"id":"8328162e-fd71-2150-dc13-71ff5bd562ed","cardType":"basic","points":1,"front":"Round 82.319 to 2 decimal places.","back":"82.32","mcqOptions":[{"text":"82.32","correct":true,"explanation":"Two decimal places retain the tenths digit 3 and hundredths digit 1. The next digit is 9, so the hundredths digit rounds up to 2."},{"text":"82.31","correct":false,"explanation":"This truncates the number after two decimal places instead of rounding it. The next digit is 9, so the hundredths digit increases, giving 82.32."},{"text":"82.3","correct":false,"explanation":"This gives only one decimal place because just the tenths digit remains. Two decimal places are required, and rounding using the 9 gives 82.32."},{"text":"82.319","correct":false,"explanation":"This leaves the original number unchanged at three decimal places. Rounding to two decimal places uses the third decimal digit, producing 82.32."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Rounding","title":"Rounding Flashcards","topbar":{"backHref":"/gcse/maths/ocr/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"d3456a36-bccf-469d-86d2-cc4cb2dba6e0","walled":"$L39"}],"$L3a","$L3b"]