Decimals - ACT Math

Card 0 of 747

Question

Convert 0.825 into a fraction.

Answer

0.825 in fraction form is $\frac{825}{1000}$ . Simplifying the fraction equals $\frac{33}{40}$ .

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Question

What is the fraction value of the decimal 0.11?

Answer

If we were to divide 1 by the decimal value we get:

$\frac{1}{0.11}\approx9$

From this we can determine that 1 is our numerator and 9 is our denominator, giving us:

$\frac{1}{9}$

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Question

If $\frac{1}{3} < x < 0.76$ , can equal which of the following?

Answer

Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.

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Question

Simplify:

$0.35+\frac{0.75}{0.2}-0.4*\frac{0.5}{0.1}$

Answer

Begin by multiplying all of your decimal fractions by $\frac{100}{100}$ :

$0.35+\frac{0.75}{0.2}\frac{100}{100}-0.4\frac{0.5}{0.1}\frac{100}{100}$

Simplify:

$0.35+\frac{75}{20}-0.4\frac{50}{10}=0.35+\frac{15}{4}-0.45$

Now perform the multiplication:

$0.35+\frac{15}{4}-2$

The easiest thing to do next is to subtract from :

$0.35+\frac{15}{4}-2=\frac{15}{4}-1.65$

Next, convert into the fraction $\frac{165}{100}$ :

$\frac{15}{4}-\frac{165}{100}$

Now, the common denominator can be :

$\frac{15}{4}\frac{25}{25}-\frac{165}{100}=\frac{375}{100}-\frac{165}{100}$

Simplify:

$\frac{375}{100}-\frac{165}{100}=\frac{210}{100}=\frac{21}{10}$

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Question

Find the sum of the following:

$5\frac{1}{8}+6\frac{3}{16}?$

Answer

To get the decimal from a fraction, divide the numerator by the denominator

$\frac{1}{8}=0.125$

$5\frac{1}{8}=5.125$

$\frac{3}{16}=0.1875$

$6\frac{3}{16}=6.1875$

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Question

When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?

Answer

When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).

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Question

Find the sum to the nearest hundredth:

$13\frac{3}{8} + 12\frac{17}{40} ?$

Answer

1. Convert the fractions to decimals by division:

$\frac{3}{8}=0.375$

$\frac{17}{40}=0.425$

2. Add the corresponding whole numbers to the decimals:

3. Add the two decimals:

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Question

Write 0.45 as a fraction.

Answer

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

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Question

What is equivalent to?

Answer

We need to convert into a fraction.

To do this, write down $\frac{0.48}{1}$

Now, because the decimal goes to the hundreth place, multiply the numerator and denominator of the fraction by 100.

$\frac{0.48\times100}{1\times100}=\frac{48}{100}$

Now, simplify the fraction.

$\frac{48}{100}=\frac{24}{50}$

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Question

Convert this decimal to a fraction in reduced form:

$\large 0.3\overline{6}$

Answer

To figure out what fraction this decimal corresponds to, we have to get rid of the repeating part, otherwise we would be dealing with an infinite recursion and we don't have the tools to deal with that yet. Instead, we will set the decimal equal to and multiply it by 10, and also multiply it by 100.

$x = 0.3\overline{6}{}$

$10x=3.\overline{6}{}$

$100x = 36.\overline{6}{}$

Notice that in and we have the same repeating decimal part. So if we subtract them, it disappears:

Now all that remains is to do the algebra.

$x=\frac{33}{90} = \frac{11}{30}{}$

$\frac{11}{30}{}$ is our final answer.

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Question

A tub of food contains pounds of vegetables, pounds of lard, and pounds of sausage. What is its total weight as an improper fraction?

Answer

To begin with, it is easiest just to add these decimals together using your calculator:

Now, this is the same thing as:

We can rewrite this:

$17 + \frac{1}{4}$

To find this, you need to give the two numbers a common denominator:

$17 + \frac{1}{4} = \frac{68}{4}+\frac{1}{4}=\frac{69}{4}$

This is your answer.

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Question

What is the fractional equivalent of ?

Answer

In decimal form is said 33 hundredths.

This is equal to

$\frac{33}{100}$ .

This fraction cannot be reduced any further therefore it is in its final answer form.

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Question

What is the fractional equivalent of ?

Answer

To find the fractional equivalent of a decimal, set the decimal as a fraction over , then multiply top and bottom by one power of for each digit after the decimal. In this case, we have two digits after the decimal, so we multiply top and bottom by :

$3.14 = \frac{3.14}{1} = \frac{314}{100}$

Now, start simplifying.

$\frac{314}{100} = \frac{157}{50}$

Since we cannot reduce further, $3.14 = \frac{157}{50}$ .

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Question

Find the square root of the following decimal:

$\sqrt{.00081}=$

Answer

The easiest way to find the square root of a fraction is to convert it into scientific notation.

$\dpi{100} \small .00081 = 8.1 \times 10^{-4}$

The key is that the exponent in scientific notation has to be even for a square root because the square root of an exponent is diving it by two. The square root of 9 is 3, so the square root of 8.1 is a little bit less than 3, around 2.8

$\dpi{100} \small \sqrt{8.1 \times 10^{-4}} \approx 2.8 \times 10^{-2} \approx 0.028$

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Question

Find the square root of the following decimal:

$\small \sqrt{0.0049}$

Answer

To find the square root of this decimal we convert it into scientific notation.

$\small 0.0049 = 49 \cdot10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root.

$\small \sqrt{0.0049} = \sqrt{49}\cdot\sqrt{10^{-4}} = 7\cdot10^{-2} = 0.07$

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Question

Find the square root of the following decimal:

$\small \sqrt{0.025}$

Answer

This problem can be solve more easily by rewriting the decimal into scientific notation.

$\small 0.025 = 2.5 \times 10^{-2}$

Because $\small 10^{-2}$ has an even exponent, we can take the square root of it by dividing it by 2. The square root of 4 is 2, and the square root of 1 is 1, so the square root of 2.5 is less than 2 and greater than 1.

$\small \sqrt{0.025} = \sqrt{2.5}\times \sqrt{10^{-2}} = 1.58\times 10^{-1} = 0.158$

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Question

Find the square root of the following decimal:

$\small \sqrt{0.00036}$

Answer

This problem becomes much simpler if we rewrite the decimal in scientific notation

$\small 0.00036 = 3.6\times 10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can take its square root by dividing it by two. The square root of 4 is 2, and because 3.6 is a little smaller than 4, its square root is a little smaller than 2, around 1.9

$\small \sqrt{0.025} = \sqrt{3.6}\times \sqrt{10^{-4}} \approx 1.9\times 10^{-2} = 0.019$

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Question

Find the square root of the following decimal:

$\small \sqrt{0.00000025}$

Answer

To find the square root of this decimal we convert it into scientific notation.

$\small \small 0.00000025 = 25 \times 10^{-8}$

Because $\small \small 10^{-8}$ has an even exponent, we can divide the exponenet by 2 to get its square root. $\small 25$ is a perfect square, whose square root is $\small 5$ .

$\small \small \sqrt{0.00000025} = \sqrt{25}\times \sqrt{10^{-8}} = 5\times10^{-4} = 0.0005$

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Question

Jenny is getting ready for school. She bought school supplies on a tax-free day. She bought notebooks for $1.25 each and crayons for $0.90 each. Jenny bought two more notebooks than crayons. She paid with a ten dollar bill and got $1.05 in change. How many notebooks did she buy?

Answer

Define variables as x = number of crayons and x + 2 = number of notebooks

To find out how much she spent, we subtract her change from what she paid with: 10.00 – 1.05 = 8.95

Then we need to solve the problem cost of notebooks plus the cost of crayons equals the total cost.

1.25(x + 2) + 0.90x = 8.95 and solving for x gives 3 crayons and 5 notebooks

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Question

Find the square root of the following decimal:

$\small \sqrt{0.0169}$

Answer

To find the square root of this decimal we convert it into scientific notation.

$\small \small 0.0169 = 169\times10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. $\small 169$ is a perfect square, whose square root is $\small 13$ .

$\small \small \sqrt{0.0169} = \sqrt{169}\times \sqrt{10^{-4}} =13\times10^{-2} = 0.13$

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