Decimals and fractions

Fractions and decimals are two ways to show the same amount. To turn a fraction into a decimal, look at the bottom number. If it is 10, the decimal has one digit after the point. So 7/10 = 0.7. If the bottom number is 100, the decimal has two digits after the point. So 25/100 = 0.25. Money works the same way. One pound is 100p, so 50p is 0.50 of a pound, and 5p is 0.05 of a pound. To turn a decimal back into a fraction, say the decimal out loud. 0.3 is three tenths, which writes as 3/10. 0.45 is forty five hundredths, which writes as 45/100, and that simplifies to 9/20. Try it with 0.75. Say it out loud: seventy five hundredths. Write 75/100, then simplify by dividing top and bottom by 25 to get 3/4. With a little practice you will recognize the common ones right away: 1/2 is 0.5, 1/4 is 0.25, and 3/4 is 0.75.

When you add or subtract decimals, the golden rule is to line up the decimal points. Write the numbers one above the other so the points sit in a straight line, then add or subtract as normal. The point in your answer goes right below the other points. Try 2.50 take away 0.75. Write 2.50 on top and 0.75 below it, points lined up. You need to borrow to do the hundredths: 0 hundredths becomes 10, and 10 take away 5 is 5. Then 4 tenths take away 7 tenths needs another borrow, leaving 14 tenths take away 7 tenths, which is 7. Finally 1 whole take away 0 is 1. The answer is 1.75. This skill is super handy with money, because pounds and pence are decimals. £2.50 minus 75p is really 2.50 minus 0.75, which is £1.75. It also works for measures. A rope 2.5 m long with 0.75 m cut off leaves 1.75 m. Line up the points, borrow carefully, and decimals behave just like whole numbers.

The metric system is built on powers of 10, which makes converting measures feel just like moving a decimal point. To change to a smaller unit, multiply by 10, 100, or 1000. To change to a bigger unit, divide by 10, 100, or 1000. 4.56 m = 456 cm, because 1 m is 100 cm and 4.56 × 100 = 456. Think about whether the new number should grow or shrink. Centimetres are smaller than metres, so you need more of them, and the number gets bigger. Grams are smaller than kilograms too. 1 kg = 1000 g, so 0.3 kg = 300 g because 0.3 × 1000 = 300. Going the other way, kilograms are bigger than grams, so the number shrinks: 750 g = 0.75 kg because 750 ÷ 1000 = 0.75. Ask yourself two questions: which unit is smaller, and do I multiply or divide? Smaller unit means multiply, bigger unit means divide, and the 10s do the rest.

To turn a fraction into a decimal, divide the top number by the bottom number. If the fraction is a top heavy one like 2 and 1/2, the whole number stays in front of the point. Let us try 2/5. Write it as 2 ÷ 5. Five is too big to go into 2, so put a point and a zero after the 2 to make 2.0. Now 5 goes into 20 exactly 4 times, with nothing left over. So 2/5 = 0.4. Some fractions never quite finish, like 1/3 = 0.333... and that is fine, you just round them when you need to. The ones with 10 or 100 on the bottom are the friendliest. 3/10 = 0.3 and 7/100 = 0.07. Those pop up all the time in money and measuring, so they are worth knowing by heart. Practice by picking fractions like 3/4 or 1/2, dividing top by bottom, and checking that your decimal makes sense. 3/4 should be close to 1, and 0.75 is.

A ruler is really a number line for measuring length. To build one, you split a strip into equal parts, and each part is a unit fraction of an inch. Start at 0 and mark equal spaces. Mark every 1 unit for whole inches, every 1/2 inch for halves, and every 1/4 inch for quarters. Those fractions have decimal names. 1 is 1.0, 1/2 is 0.5, and 1/4 is 0.25. So when you measure a paperclip and it reaches the second quarter inch mark, you can say it is 1 and 1/4 inches, or 1.25 inches. Both names tell the same length. To make your own ruler, fold a paper strip in half to find 1/2, then fold it in half again to find the quarters. Label 0, 0.25, 0.5, 0.75, and 1. Now you can measure small things and read the length as either a fraction or a decimal, just like the marks on a real ruler.