Rational Vs Irrational
Which number is irrational?
A. 0.75
B. √18
C. −7/2
D. √49
B. √18 Irrational because it is not a perfect square.
2³ × 2⁴
2⁷
What is 3/4 as a decimal?
.75
Between which consecutive integers is √45?
6 and 7
Write 3.6 × 10⁵ in standard form
360,000
Simplify 5⁶ ÷ 5³.
53
Write .666666 as a fraction
6/9 or 2/3
∛(−125)
-5
Write 0.000084 in scientific notation.
8.4 x 10-5
(3²)³
36
Convert 7/8 to a decimal.
.875
Evaluate ∛(1/8)
1/2
Calculate (2 × 10⁴)(3 × 10³). Express in scientific notation.
6 x 107
What is 4⁻²
1/16
Order from least to greatest: −√9, −2.7, −11/4, −2.6.
Answer: −√9, −11/4, −2.7, −2.6
A student says √50 = 25 because 25 × 2 = 50. Explain the error and estimate √50 to the nearest tenth.
The student incorrectly divided 50 by 2 instead of finding a number that multiplies by itself to equal 50.
√50 ≈ 7.071
Calculate (8.4 × 10⁶) ÷ (2.1 × 10²). Express in scientific notation.
4 x 104
Explain why 0.375 is rational. Write it as a fraction in simplest form.
375/1000 or 3/8 it can be written as a fraction
A student simplifies 7² × 7³ as 49⁵. Explain the mistake and give the correct power of 7.
The student incorrectly multiplied the bases. When multiplying powers with the same base, keep the base and add the exponents.
75
Order √10, 3.4, and 10/3 from least to greatest. Show approximate decimals.
√10 ≈ 3.162
10/3 ≈ 3.333
3.4 = 3.4
A square garden has an area of 64 square feet. Find the side length.
8 feet
A student claims 5 × 10⁻³ > 2 × 10⁻² because 5 > 2. Explain using decimals.
5 × 10⁻³ = 0.005
2 × 10⁻² = 0.02
Answer: The student is incorrect because 0.005 is less than 0.02. The exponent affects the value, not just the coefficient.