PSAT Math - How to divide decimals

simplify: 0.2 ÷ 0.04

0.005

0.05

0.02

Explanation

0.2 ÷ 0.04 <- easiest way to approach is to move the decimal to the right (the same amount of spaces on each side) so that the decimal disappears

since 0.04 has 2 spaces and 0.2 only has 1, move the decimal 2 spaces to the right on each side

0.2 ÷ 0.04 = 20 ÷ 4 = 5

23 grams of sodium are equal to $6.022 \times 10^{23}$ atoms. How many atoms comprise one milligram of sodium?

(Select the closest answer)

$2.62 \times 10^{19}$

$2.62 \times 10^{18}$

$2.62 \times 10^{17}$

$1.39 \times 10 ^{20}$

$1.39 \times 10 ^{19}$

Explanation

23 grams are equal to 23,000 milligrams, so to find the number of atoms in one milligram, divide:

$=\frac{ 6.022 \times 10^{23} }{ 23,000}$

$=\frac{ 6.022 \times 10^{23} }{ 2.3 \times 10 ^{4} }$

$= \frac{ 6.022 }{ 2.3 } \cdot \frac{ 10^{23} }{ 10 ^{4} }$

$=2.62 \times 10^{19}$

Simplify:

$\frac{0.004}{0.0005}$

Explanation

Multiply both the numerator and denominator by some power of 10 to get rid of the decimals; in this case, multiply both by 10,000.

$\frac{0.004}{0.0005}\cdot \frac{10,000}{10,000}=\frac{40}{5}=8$

Which number has 2.8 as its reciprocal?

$\frac{5}{1 4}$

$-\frac{5}{1 4}$

Explanation

The number that has 2.8 as its reciprocal is, in return, the reciprocal of 2.8.

$2.8 = \frac{28}{10} = \frac{28 \div 2}{10 \div 2} = \frac{14}{5}$

The reciprocal of this can be found by switching the numerator and the denominator. This is $\frac{5}{1 4}$ .

If the cost of 20 equally priced pencils cost $5.80, then at the same rate what is the greatest number of pencils you can purchase for $50?

172

173

172.41

200

150

Explanation

Remeber for this problem that you cannot spend more than $50. First find the price of each pencil by 5.80/20 = 29 cents. And then use this to do 50/0.29 = 172.41. So the greatest number of pencils you can purchase for $50 is 172 pencils.

Charlie has charges on his credit card of $63.70, $37.32, and $81.78. If he pays down half his bill at once, and then pays the rest in four equal monthly installments, how much is each monthly installment?