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 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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