Grade 8 · Math · Unit 1 of 18
Big, Small & Real Numbers
Scientific notation and irrational numbers
What your child practises
Writing very large and very small numbers in scientific notation, telling rational from irrational numbers, ordering numbers such as √2 and π, and mentally multiplying and dividing by powers of ten.
Ontario Curriculum expectation: B1.1, B1.2, B2.3 · scientific notation, rational and irrational numbers, and multiplying and dividing by powers of ten
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Which number is rational?
- √7
- −3/4
- √2
- √5
Show answer
−3/4
Hint: A rational number can be written as a fraction of two integers. Square roots of perfect squares, like √49 = 7, are rational.
Question 2
Write 0.056 in scientific notation (a number from 1 up to 10, times a power of 10).
- 5.6 × 10⁻¹
- 56 × 10⁻³
- 5.6 × 10⁻²
- 5.6 × 10²
Show answer
5.6 × 10⁻²
Hint: Count how many places the decimal point moves to get a number from 1 to 10. Moving right makes the exponent negative.
Question 3
A scientist writes 6.02 × 10²³. What does the exponent 23 tell you?
- The number has 23 digits before the decimal point.
- The decimal point moves 23 places to the right.
- The decimal point moves 23 places to the left.
- Multiply 6.02 by 23.
Show answer
The decimal point moves 23 places to the right.
Hint: The exponent counts how many places the decimal point moves. A positive exponent moves it right.
Question 4
Which is the least number?
- 3.6 × 10²
- 3.2 × 10⁴
- 6.1 × 10⁻⁶
Show answer
6.1 × 10⁻⁶
Hint: Compare the exponents first. A greater exponent means a greater number, whatever the first number is.
Question 5
Use mental math. What is 0.596 × 1000?
0.596 × 1000 = ?
answer box
Show answer
596
Hint: Multiplying by 1000 moves the decimal point 3 places to the right.
Question 6
Use mental math. What is 0.63 × 10?
0.63 × 10 = ?
answer box
Show answer
6.3
Hint: Multiplying by 10 moves the decimal point 1 place to the right.