8th grade · Math · Unit 5 of 17
Big, Small & Real Numbers
Scientific notation and irrational numbers
What your child practices
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.
Alaska content standards learning standard: 8.NS.1; 8.NS.2; 8.EE.3; 8.EE.4 · irrational numbers and scientific notation
How we explain it
Children can open this short lesson before they practice.
- Scientific notation writes a number as a number from 1 to 10 times a power of 10.
- Multiplying by 10³ moves the decimal point 3 places right.
- Irrational numbers, like π, cannot be written as a fraction.
Example: Write 45,000 in scientific notation. Move the point 4 places left: 4.5. So 45,000 = 4.5 × 10⁴. Answer: 4.5 × 10⁴
Big, Small & Real Numbers in Alaska
In the Alaska content standards, this is unit 5 of 17 in 8th grade Math, after Surface Area & Volume and before Scatter Plots & Stories.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Alaska Department of Education and Early Development
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
Use mental math. What is 8.6 ÷ 10?
8.6 ÷ 10 = ?
answer box
0.86
Hint: Dividing by 10 moves the decimal point 1 place to the left.
Question 2
Tap the numbers from least to greatest.
- −√5
- √5
- √2
- π
−√5 → √2 → √5 → π
Hint: Estimate each square root: √2 is about 1.4, √5 about 2.2, √10 about 3.2. Negative numbers come first.
Question 3
Which is the least number?
- 6.1 × 10⁴
- 9.5 × 10⁻⁴
- 9.5 × 10⁸
9.5 × 10⁻⁴
Hint: Compare the exponents first. A greater exponent means a greater number, whatever the first number is.
Question 4
Which describes 0.333… (the 3 repeats forever)?
- rational, because it equals 1/3
- an integer
- irrational, because it never ends
- not a real number
rational, because it equals 1/3
Hint: A repeating decimal is rational because it can be written as a fraction.
Question 5
Which number is rational?
- −0.6
- √2
- √5
- √11
−0.6
Hint: A rational number can be written as a fraction of two integers. Square roots of perfect squares, like √49 = 7, are rational.
Question 6
Compared with 1.5 × 10⁹ m, a distance of 1.5 × 10¹¹ m is…
- 1.5 times as far
- 2 times as far
- 100 times as far
- 10 times as far
100 times as far
Hint: Subtract the exponents: 11 − 9 = 2, so it is 10² = 100 times as much.