Multiples of 10 involving negative exponents | Maths | Quizalize & Oak National Academy

Starter quiz

A prime number is an integer greater than one with exactly ______ factors.
- '2' ✓
Which of the following products only use prime numbers?
- 2 × 2 × 13 ✓
- 2 × 6 × 13
- 2 × 9 × 13
- 2 × 3 × 5 × 17 ✓
Write 300 as a product of its prime factors.
- 4 × 3 × 25
- 2² × 3 × 5² ✓
- 4 × 3 × 5²
- 2² × 3 × 25
- 2² × 3 × 5
Use the fact that 60 = 2² × 3 × 5 to write 300 as a product of its prime factors.
- 2² × 3² × 5
- 2² × 3 × 5² ✓
- 2² × 3² × 5²
- 2 × 3 × 5²
Use the fact that 60 = 2² × 3 × 5 to write 30 as a product of its prime factors.
- 2² × 3 × 5 ÷ 2
- 2 × 3 × 5 ✓
- 2² × 5
- 2 × 3 × 5²
If 52 = 2² × 13 and 175 = 5² × 7, which of the following is the most useful arrangement to calculate 175 × 52?
- 2 × 2 × 13 × 5 × 5 × 7
- 2 × 13 × 2 × 5 × 5 × 7
- 2 × 5 × 2 × 5 × 13 × 7 ✓
- 2 × 7 × 2 × 5 × 13 × 5

A number written in exponential form represents a repeated ...
- addition
- division
- multiplication ✓
- subtraction
Match each fraction to its equivalent exponential form.
- ${1}\over{10}$
  
  ⇔
  
  $10^{-1}$ ✓
- ${1}\over{100}$
  
  ⇔
  
  $10^{-2}$ ✓
- ${1}\over{1000}$
  
  ⇔
  
  $10^{-3}$ ✓
- ${1}\over{10 000}$
  
  ⇔
  
  $10^{-4}$ ✓
- ${1}\over{100 000}$
  
  ⇔
  
  $10^{-5}$ ✓
- ${1}\over{1 000 000}$
  
  ⇔
  
  $10^{-6}$ ✓
Match each decimal to its equivalent exponential form.
- $0.002$
  
  ⇔
  
  $2\times10^{-3}$ ✓
- $0.00004$
  
  ⇔
  
  $4\times10^{-5}$ ✓
- $0.2$
  
  ⇔
  
  $2\times10^{-1}$ ✓
- $0.005$
  
  ⇔
  
  $5\times10^{-3}$ ✓
- $0.000005$
  
  ⇔
  
  $5\times10^{-6}$ ✓
- $0.0004$
  
  ⇔
  
  $4\times10^{-4}$ ✓
$3\times10^{-2}+2\times10^{-5}+8\times10^{-6}$ represents the number ______
- '0.030028' ✓
Which of the following is not an alternative way of writing 2400?
- $24\times10^2$
- $24 000\div10$
- $240 000\div10^3$ ✓
- $2.4\times10^3$
- ${{240}\over{10}}\times10^2$
Which of the following is not an alternative way of writing 12 000?
- $1.2\times10^3$ ✓
- ${{1200}\over{10^2}}\times10^3$
- $120 000\times10^{-1}$
- $1.2\times10^4$
- ${{120}\over{10^3}}\times10^4$ ✓

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A positive exponent tells you how many identical values must be multiplied together.
Dividing by 10^n is the same as multiplying by its reciprocal.
A negative exponent tells you how many reciprocals of the base must be multiplied together.
a^(−3) = 1/a^3

A negative exponent implies that the entire value is negative.

Refer back to the table showing the structure of how the negative exponents occur and highlight that none of the decimal values are negative.

Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.