Work out (3.2 × 105) – (2.89 × 104) Give your answer in standard form Classwork/Homework Work out (3.2 × 105) – (2.89 × 104) Give your answer in standard form b) Write the biggest number and the smallest number as an ordinary number: c) Work out 4 x 108 x 5 x 10-6.Give your answer in standard form d) Work out 7 x 103 x 2 x 10-5.Give your answer in standard form 8.3 x 104 3.9 x 105 6.7 x 10-3 9.245 x 10-1 8.36 x 103 4.15 x 10-2

Work out (3.2 × 105) – (2.89 × 104) Give your answer in standard form Classwork/Homework Work out (3.2 × 105) – (2.89 × 104) Give your answer in standard form 320000 – 28900 = 291100 291100  2.911 x 105 b) Write the biggest number and the smallest number as an ordinary number: 83000 390000 0.0067 0.9245 8360 0.0415

Classwork/Homework c) Work out 4 x 108 x 5 x 10-6.Give your answer in standard form (4 x 5) x (108 x 10-6) (20) x (108+-6) 20 x 102 2 x 103 (2 + 1 = 3) Answer: 2 x 103

Classwork/Homework d) Work out 7 x 103 x 2 x 10-5.Give your answer in standard form (7 x 2) x (103 x 10-5) (14) x (103+-5) 14 x 10-2 1.4 x 10-1 (-2 + 1 = -1) Answer: 1.4 x 10-1

N E T S A T O M I I T O M I X P O P A N I R D O N G U N I R Guess the Anagrams N E T S A T O M I I T O M I X P O P A N I R D O N G U N I R What do they mean? Why are they useful?

0.003  leading zeros are not considered significant Significant Figures Significant figures are those numbers considered to be important because they give you useful information All non-zero digits are significant Zeros aren’t always significant – it depends on their position in the number Zeros before the first non-zero digit are not significant 203  significant 0.003  leading zeros are not considered significant To compare two numbers you would need the 3 To compare two numbers for 203 the 0 plays an important role

Significant Figures The first significant figure is always the first non-zero digit you come across (from left to right) The second significant figure is the digit next to the first significant figure and so on. We often shorten significant figures to s.f.

The second, third and fourth significant figures are the digits immediately following the first significant figure, including zeros. For example, 4 890 351 This is the first significant figure 4 890 351 4 890 351 This is the third significant figure 0.0007506 0.0007506 This is the second significant figure 4 890 351 4 890 351 This is the fourth significant figure 0.0007506 and 0.0007506 This is the first significant figure 0.0007506

Important Point When rounding to a number of significant figures: The size of your rounded number (your answer) should be a similar size to the number in the question! Ex. Round 32560  Answer 33 YOU CANT BE ASKED TO ROUND 32560 AND THE ANSWER IS 30 !

ALL THE NUMBERS AFTER WILL BECOME ZERO Significant Figures Round 17.46789 to 2 significant figures 2nd significant figure, this will stay a 7 or go to 8 depending on what the next number is 1st significant figure ALL THE NUMBERS AFTER WILL BECOME ZERO Round 17.46789 to 2 significant figures= 17.00000 or just 17!

It’s more than 4 so we round up! Round to 1 s.f. 3 7 8 5 4 3 7 Look at the next number It’s more than 4 so we round up!

It’s less than 5 so we round down! Round to 3 s.f. 3 7 8 4 3 7 Look at the next number It’s less than 5 so we round down!

It’s more than 4 so we round up! Round to 2 s.f. . 2 9 8 9 Look at the next number It’s more than 4 so we round up!

It’s more than 4 so we round up! Round to 3 s.f. . 2 9 8 7 Look at the next number It’s more than 4 so we round up!

Note If you are rounding to say 3 significant figures, the answer must have AT LEAST 3 significant figures!

Homework STUDY what we have covered so far WORKING WITH NUMBERS Positive indices (find the value & write index form) Multiplying and Dividing Indices Negative and Zero Indices Standard form (big numbers) Standard form (small numbers) Rounding to Significant Figures