DECIMALS

• Place Value• Ordering Decimals• Nearest and significant figures• Money• Adding and Subtracting• Multiplying and dividing by

10,100,1000 etc• Multiplying• Dividing

Place Value

• Similar to whole numbers the position of the digit indicates how big it is.

• If it is in the first column after the decimal it is in the ‘tenths’ column

Place Value

• 0.053• The 5 here means

5 hundredths• 0.053• The 3 here means

3 thousandths• 32.4• The 4 here means

4 tenths

Ordering Decimals

• Comparing decimal numbers requires looking at the place value of the digits.

• Firstly compare the whole number part.

• If the whole number part is the same the decimal part must be investigated.

• Which is bigger 125.36785 or 125.37?

• The whole number parts are both 125 so we must check decimal part.

Ordering Decimals

• Look at the ‘tenths’ column. Whichever number has the higher digit that is the bigger number.

• If they are the same move on to the ‘hundredth’ column

• Continue until the order is sorted.

• Which is bigger 125.36785 or 125.37?

• They both have 3 in the tenths column.

• In the hundredths column we have 6 and 7.

• This means 125.37 is bigger even though 125.36785 is longer

Nearest Decimal Place• Sometimes a decimal

number is too long• We need to chop it off

after a certain number of places

• Lets look at 125.36785• If we want only 2

numbers after the decimal point we have two choices

• The number is either 125.36 or 125.37

• Which one?• We must look at the

next number • 125.367• 7 is closer to10 than 0• We round up and

choose 125.37• If the number is 5 or

more round up• If it is 4 or less round

down

Significant figures

• Significant figures is similar to nearest place

• Except we are only interested in the first few digits and the rest we round to zeroes

• E.g. When talking about populations we are only interested in millions

• What is 1253678 to 2 significant figures

• We are only looking at the first two digits and rounding the rest to zeroes

• 1200000 or 1300000• 1253678 • The third number is 5

so we round up• Answer is 1300000

Money

• Money is represented by numbers to two decimal places

• If writing out in pounds DO NOT put in the p sign

• Two pounds fifty pence is written £2.50 not £2.50p

• When dividing money among people the answer should be rounded up to two decimal places to make sure the money is covered.

Adding and subtracting

• Adding and subtracting is the same as whole numbers

• Just line up the decimal points.

Multiplying by 10,100, etc

• Multiplying by 10 move the decimal point one place to the right.

• Multiplying by 100 move the decimal two places to the left.

• Move the decimal as many places to the left as there are zeroes

• 4.15 x 10 = 41.5

• 4.15 x 100 = 415

• 4.15 x 1000 = 4150

Dividing by 10, 100,etc

• Dividing by 10 move the decimal point one place to the left

• Dividing by 100 move the decimal two places to the right

• Move the decimal as many places to the right as there are zeroes

• 4.15 / 10 = 0.415

• 4.15 / 100 = 0.0415

• 4.15 / 1000 = 0.00415

Multiplying (25.6 x 2.67)

Multiply as normal ignoring the decimals

• Count how many numbers after the decimal points in the two numbers

• The answer will have the same number of decimal places

• 256 x 267 = 68352

• 25.6 ( One number )• 2.67 ( Two numbers )• Three numbers in

total• • Ans = 68.352

• 2.56 x 2.67 = 6.8352

Dividing decimals by a whole number (542.1 / 3)

• When dividing by a whole number place the decimal point in the answer above the point in the question

• Divide as normal

Dividing decimals by another decimal

• It is not a good idea to divide one decimal by another as confusion arises as to where to put the decimal point

• Instead we will convert the dividing number to a whole number by moving the decimal

• 16.125 / 3.75• Move the decimal

points two places to the right to change 3.75 to 375

• The new division becomes

• 1612.5 / 375• Now divide as normal

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