Standard form

Question 1

Work out 3.2 × 10⁵ + 8.7×10⁶ =

Answer 1

3.2×10⁵
32,320,3200,32000,320000
320000

8.7×10⁶
87,870,8700,87000,870000,8700000
8700000

8 700 000 + 320 000= 9 000 020
9.02,90.2,902,9020,90 020,900 020
9 000 020
Answer = 9.02 × 10⁶

Question 2

Work out 5.8 ×10⁷ + 9.4×10⁶

Answer 2

5.8×10⁷
58,580,5800,58000,580 000,5 800 000, 58 000 000
= 58 000 000

9.4×10⁶
94,940,9400,94 000, 940 000, 9 400 000
= 9 400 000

58 000 000 + 9 400 000 = 67 400 000

674,6740,67 400, 674 000, 6 74 000, 67 400 000

Answer= 6.7 × 10⁶

Question 3

Work out the value of 3 × 10⁴ × 4×10⁶
Give your answer in standard form

Answer 3

Step 1) Multiply 3 × 4 = 12
Step 2) Add the powers 6+4=10
Step 3) Now it’s 12×10¹⁰
Step 4) However because there are 2 lots of 10 in the multiplication it will be 12×10¹×10¹⁰
Step 5) Add the powers so now it’s 12 ×10¹¹
Step 6) Divide 12 by 10 which is 1.2

Answer = 1.2×10¹¹

Question 4

Work out the value of 6×10³ × 7×10⁸
Give your answer in standard form

Answer 4

Step 1) 6 x 7 which is 42
Step 2) Add the powers 3+8=11
Step 3) 42×10¹×10¹¹
Step 4) 42×10¹²
Step 5) 42÷10=4.2
Answer = 4.2×10¹²

Question 5

Work out (8×10⁹) ÷ (2×10⁶)
Give your answer in standard form

Answer 5

Step 1) 8÷2=4
Step 2) Unlike when you multiply the numbers so you have to add the powers. When you divide numbers you subtract the powers
9 - 6 = 3
Answer= 4×10³

Question 6

Work out (6.3 × 10⁷) ÷ (2.1 × 10³)
Give your answer in standard form

Answer 6

Step 1) 6.3 × 2.1 = 13.23
Step 2) Subtract the powers 7 - 3= 4
13.23 × 10¹ × 10⁴

Answer = 13.23×10⁵