Basic Numbers 8Faae1
1. The problem asks to find all factors of 39.
Factors are numbers that divide 39 exactly without leaving a remainder.
Since 39 = 3 × 13, the factors are 1, 3, 13, and 39.
2. Estimate the value of \( \frac{6.7 \times 2.1}{18 - 5.9} \) by rounding each number to 1 significant figure.
- Round 6.7 to 7
- Round 2.1 to 2
- Round 18 to 20
- Round 5.9 to 6
Calculate numerator: \(7 \times 2 = 14\)
Calculate denominator: \(20 - 6 = 14\)
Estimate: \(\frac{14}{14} = 1\)
3. Order the numbers 0.329, \(\frac{9}{27}\), 30%, and \(\frac{3}{8}\) from smallest to largest.
Convert all to decimals:
- 0.329 stays 0.329
- \(\frac{9}{27} = 0.333...\)
- 30% = 0.30
- \(\frac{3}{8} = 0.375\)
Order: 0.30, 0.329, 0.333..., 0.375
So in original form: 30%, 0.329, \(\frac{9}{27}\), \(\frac{3}{8}\)
4. (a) Write 67200000 in standard form.
Standard form is \(a \times 10^n\) where \(1 \leq a < 10\).
\(67200000 = 6.72 \times 10^7\)
(b) Calculate \((3 \times 10^4) \times 100\) and give the answer in standard form.
Rewrite 100 as \(10^2\).
Multiply: \(3 \times 10^4 \times 10^2 = 3 \times 10^{4+2} = 3 \times 10^6\)
5. A regular polygon has 8 sides.
(a) The name of an 8-sided polygon is an octagon.
(b) The size of one exterior angle of a regular polygon is given by \(\frac{360^\circ}{n}\), where \(n\) is the number of sides.
Calculate: \(\frac{360^\circ}{8} = 45^\circ\)
Final answers:
1. Factors of 39: 1, 3, 13, 39
2. Estimate: 1
3. Order smallest to largest: 30%, 0.329, 9/27, 3/8
4. (a) \(6.72 \times 10^7\)
(b) \(3 \times 10^6\)
5. (a) Octagon
(b) \(45^\circ\)