Decimals http://www.mathsisfun.com/fractions.html

Decimals Learning Intentions place decimals in number order add and subtract decimals multiply and divide by decimals round decimals to a specified number of places convert decimals to fractions and vice versa

Number Place Value Our number system is base 10. Each number written in a column to the left is 10 times bigger Number to the left of the decimal point are bigger than or equal to 1 Numbers to the right of the decimal point are less than 1 The names of the columns are: Hundreds Tens Units tenths hundredths thousandths

The Value of a Digit Write in words the value of the digit 5 in each of the following numbers: 45.33 122.456 61.509 144.435

Adding Decimals When adding decimals the decimal points in each number must line up Add the following decimal numbers: 2.21 + 7.994 13.65 + 7.0026 + 0.6

Subtracting Decimals When subtracting decimals the decimal points in each number must line up It may be necessary to fill out the number with zeros Subtract the following decimal numbers: 13.334 – 6.4 8 – 0.645

Multiplying by 10, 100 and 1000 To multiply a number by 10, 100, 1000, we move the number to the left (by the number of zeros) Multiply the following numbers: 0.36 x 1000 0.0504 x 100

More Multiplying When multiplying by 30, 200, 6000, etc we first multiply by 10, 100 or 1000 and then multiply by 3, 2 and 6 respectively Multiply the following numbers 51.3 x 60 4.5 x 800 0.52 x 3000

Dividing by 10, 100, 1000 To divide a number by 10, 100, 1000, we move the number to the right (by the number of zeros) Divide the following numbers: 7.05 ÷ 1000 1573 ÷ 100

More Dividing When dividing by 30, 200, 6000, etc we first divide by 10, 100 or 1000 and then divide by 3, 2 and 6 respectively Divide the following numbers 4.75 ÷ 500 0.84 ÷ 200 144 ÷ 3000

Multiplying by Decimals To multiply a decimal by another decimal: Multiply the numbers ignoring the decimal points Count the total number of decimal places. This is where the point goes back into the answer. Multiply the following numbers 0.6 x 15 0.3 x 12.4 0.45 x 0.15

Rounding Numbers Sometimes when numbers are very large or very small we may not write all the digits. Imagine you have a choice of two jobs, both exactly the same, but one offers £11 999 and the other offers £21 995. The digit 9 and the digit 5 at the end doesn’t really matter. We sometimes round these to £12K and £22K

Small Fractions Sometimes when we work out the value of a fraction it doesn’t work out as an exact decimal. For example one third is 0.33333… We would still be here next week writing threes. We need to stop somewhere!

Decimal Places We often round numbers to a set number of decimal places For example: 0.333333 = 0.3 (1 decimal place) Write each of the following numbers to 1 decimal place 0.234 12.456 32.67

More decimal places Round each of the numbers to 2 decimal places: 0.238 1.294 2.9994 15.398 6.009 14.349999 12.23

How to Round Numbers Decide which is the last digit to keep Leave it the same if the next digit is less than 5 (this is called rounding down) But increase it by 1 if the next digit is 5 or more (this is called rounding up) Rounding to 1 decimal place 6.214 rounded to 1 dp = 6.2 (next digit is 1) 6.264 rounded to 1 dp = 6.3 (next digit is 6)

Dividing by Decimals We cannot divide by a decimal without a calculator, but we CAN change the calculation to a simpler one that will give the same answer: Each of the following calculations gives the same answer: 64 ÷ 0.8 6.4 ÷ 0.08 640 ÷ 8 Which calculation is the simplest?

Dividing by Decimals When dividing by a decimal number we decide how we can make the divisor decimal a whole number multiply BOTH decimals by this number to make the calculation easier Divide the following numbers: 0.024 ÷ 0.6 64 ÷ 0.008

Changing Fractions to Decimals To convert a fraction into a decimal, we divide the numerator by the denominator Change the following fractions into decimals

Changing Decimals into Fractions When converting a decimal into a fraction we find the lowest place value of the number write the decimal as a whole number over this number Simplify the result Change the following decimals into fractions 0.345 0.042