PLACE VALUE, ORDERING AND ROUNDING

MULTIPLYING AND DIVIDING BY 10, 100 AND 1000 Complete the following: 3.4 × 10 = ÷ = × 45.8 = × = ÷ 10 = ÷ = ÷ 1000 = × = × 100 = ÷ =

MULTIPLYING BY 0.1 AND 0.01 What is 4 × 0.1? We can think of this as 4 lots of 0.1 or We can also think of this as 4 × × is equivalent to 4 ÷ Therefore: 4 × 0.1 = 0.4 Multiplying by 0.1Dividing by 10 is the same as

DIVIDING BY 0.1 AND 0.01 What is 7 ÷ 0.1? We can think of this as “How many 0.1s (tenths) are there in 7?”. There are ten 0.1s (tenths) in each whole one. So, in 7 there are 7 × 10 tenths. Therefore: 7 ÷ 0.1 = 70 Dividing by 0.1Multiplying by 10 is the same as

POWERS OF TEN Our decimal number system is based on powers of ten. We can write powers of ten using index notation. 10 = = 10 × 10 = = 10 × 10 × 10 = = 10 × 10 × 10 × 10 = = 10 × 10 × 10 × 10 × 10 = = 10 × 10 × 10 × 10 × 10 × 10 = = 10 × 10 × 10 × 10 × 10 × 10 × 10 = 10 7 …

NEGATIVE POWERS OF TEN Any number raised to the power of 0 is 1, so 1 = 10 0 We use negative powers of ten to give us decimals = = = 10 − = = = 10 − = = = 10 − = = = 10 − = = = 10 − = = =10 −

STANDARD FORM We can write very large numbers using standard form. For example, the average distance from the earth to the sun is about km. We can write this number as 1.5 × 10 8 km. To write a number in standard form we write it as a number between 1 and 10 multiplied by a power of ten. A number between 1 and 10 A power of ten

These numbers are written in standard form. How can they be written as ordinary numbers? 5 × = × 10 6 = × = × 10 7 = × 10 3 = STANDARD FORM – WRITING LARGE NUMBERS

How can we write these numbers in standard form? = 6 × 10 − = 7.2 × 10 − = 5.02 × 10 − = 3.29 × 10 − = × 10 −3 STANDARD FORM – WRITING SMALL NUMBERS

ROUNDING WHOLE NUMBERS Complete this table: to the nearest to the nearest 100 to the nearest

ROUNDING TO A GIVEN NUMBER OF DECIMAL PLACES Complete this table: to the nearest whole number to 1 d.p.to 2 d.p.to 3 d.p

ROUNDING TO SIGNIFICANT FIGURES Numbers can also be rounded to a given number of significant figures. The first significant figure of a number is the first digit which is not a zero. For example: and This is the first significant figure This is the first significant figure

ROUNDING TO SIGNIFICANT FIGURES For example: and This is the first significant figure This is the first significant figure The second, third and fourth significant figures are the digits immediately following the first significant figure, including zeros This is the second significant figure This is the second significant figure This is the third significant figure This is the third significant figure This is the fourth significant figure This is the fourth significant figure

Complete this table: to 3 s. f to 2 s. f.to 1 s. f ROUNDING TO SIGNIFICANT FIGURES