cc77-d988-4962-973f-f840dc9dc09a:decimals","label":"Converting to Decimals","steps":[{"type":"text","order":0,"title":"Understand the method","content":"To compare these numbers easily, we will convert each of them into a **decimal**. \n\nOur original list of numbers is:\n\n$$65\\% \\quad \\text{and} \\quad \\frac{3}{5} \\quad \\text{and} \\quad 0.62 \\quad \\text{and} \\quad 0.7 \\quad \\text{and} \\quad \\frac{2}{3}$$"},{"type":"text","order":1,"title":"Convert first set","content":"Let's convert the first two numbers to decimals:\n\n* **For $65\\%$:** A percentage is a value out of $100$. To convert to a decimal, divide by $100$:\n\n$$65\\% = \\frac{65}{100} = 0.65$$\n\n* **For $\\frac{3}{5}$:** We can find an equivalent fraction with a denominator of $10$, or simply divide $3$ by $5$:\n\n$$\\frac{3}{5} = \\frac{6}{10} = 0.6$$","highlights":[{"text":"65%","location":"specification"},{"text":"3/5","location":"specification"}]},{"type":"text","order":2,"title":"Convert remaining values","content":"Now let's check the remaining numbers:\n\n* **$0.62$** is already a decimal: $$0.62$$\n* **$0.7$** is already a decimal: $$0.7 \\quad \\text{(or } 0.70 \\text{)}$$\n* **For $\\frac{2}{3}$:** Dividing $2$ by $3$ gives a recurring decimal:\n\n$$\\frac{2}{3} = 0.666... \\approx 0.67$$","highlights":[{"text":"0.62","location":"specification"},{"text":"0.7","location":"specification"},{"text":"2/3","location":"specification"}]},{"type":"text","order":3,"title":"Compare the decimals","content":"Let's list all our decimal values to easily compare them side-by-side using place value (adding a trailing zero where helpful to make them all have the same number of decimal places):\n\n$$\\begin{aligned}\n\\frac{3}{5} &\\rightarrow 0.60 \\\\\n0.62 &\\rightarrow 0.62 \\\\\n65\\% &\\rightarrow 0.65 \\\\\n\\frac{2}{3} &\\rightarrow 0.66... \\\\\n0.7 &\\rightarrow 0.70\n\\end{aligned}$$\n\nComparing the tenths and hundredths columns, we can see the order from smallest to largest is:\n\n$$0.60 < 0.62 < 0.65 < 0.66... < 0.70$$"},{"type":"text","order":4,"title":"Write original numbers","content":"Now we replace the decimal values with the numbers in their original format to write our final answer:\n\n$$\\frac{3}{5}, \\quad 0.62, \\quad 65\\%, \\quad \\frac{2}{3}, \\quad 0.7$$\n\n*This fully correct order completes both marks: converting the numbers to a common format earns the first mark M1, and writing the correct final sequence earns the second mark A1.*"}]},{"id":"c833cc77-d988-4962-973f-f840dc9dc09a:percentages","label":"Converting to Percentages","steps":[{"type":"text","order":0,"title":"Understand the goal","content":"We need to order five different numbers from smallest to largest:\n\n$$65\\%, \\quad \\frac{3}{5}, \\quad 0.62, \\quad 0.7, \\quad \\frac{2}{3}$$\n\nTo compare them easily, we will convert all of these values into **percentages** (values out of $100\\%$)."},{"type":"text","order":1,"title":"Convert first three numbers","content":"Let's convert each number to a percentage:\n\n1. **$65\\%$** is already a percentage: \n $$65\\%$$\n\n2. **$\\frac{3}{5}$**: To convert a fraction to a percentage, we can multiply by $100\\%$:\n $$\\frac{3}{5} \\times 100\\% = 3 \\times 20\\% = 60\\%$$\n\n3. **$0.62$**: To convert a decimal to a percentage, multiply by $100$ (move the decimal point two places to the right):\n $$0.62 \\times 100\\% = 62\\%$$"},{"type":"text","order":2,"title":"Convert remaining numbers","content":"Let's convert the final two numbers:\n\n4. **$0.7$**: Multiply by $100$:\n $$0.7 \\times 100\\% = 70\\%$$\n\n5. **$\\frac{2}{3}$**: Multiply by $100\\%$:\n $$\\frac{2}{3} \\times 100\\% = \\frac{200}{3}\\% = 66.\\dot{6}\\% \\approx 66.7\\%$$"},{"type":"text","order":3,"title":"Compare the percentages","content":"Now we list our converted percentages:\n- $\\frac{3}{5} = 60\\%$\n- $0.62 = 62\\%$\n- $65\\% = 65\\%$\n- $\\frac{2}{3} \\approx 66.7\\%$\n- $0.7 = 70\\%$\n\nLet's order these from smallest to largest:\n\n$$60\\% < 62\\% < 65\\% < 66.7\\% < 70\\%$$"},{"type":"text","order":4,"ti

Fractions, Decimals and Percentages

Question 7

Fractions, Decimals and Percentages Questions

Fractions, Decimals and Percentages

Question 7

Fractions, Decimals and Percentages Questions