Decimals - PSAT Math

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Question

The ogre under the bridge eats $\frac{4}{5}$ of a pizza and then throws the rest of the pizza to the rats. The rats eat $\frac{3}{4}$ of what is left. What fraction of the pizza is left when the rats are done?

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Answer

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

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Question

$\frac{1}{10}\times \frac{3}{5}\div \frac{6}{7}= {?}}$

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Answer

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

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Question

How much less is $\frac{1}{16}$ than ?

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Answer

$\frac{1}{16}=.0625$

$.0665-.0625=.004=\frac{4}{1000}=\frac{1}{250}$

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Question

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Answer

.3 can be written as .30. Now we can add the two more easily:

$\ .30$

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Question

Express as a decimal: $\frac{16}{9}$

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Answer

Divide 16 by 9:

The "7" repeats forever, so

$\frac{16}{9} = 1.\overline{7}$

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Question

Express as a decimal: $\frac{9}{16}$

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Answer

Divide 9 by 16:

$\frac{9}{16} = 0.5625$

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Question

Convert the fraction to a decimal.

$\frac{13}{25}$

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Answer

We can multiply our numerator and denominator by , which leads to $\frac{52}{100}$ . From here we divide by our denominator, moving the decimal two places to the left.

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Question

Write 0.45 as a fraction.

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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

Express as a fraction: $0.3\overline{4}$

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Answer

Let $x = 0.3\overline{4} = 0.3444...$

Then

$10 x = 10 \times 0.3444... = 3.444...$

and

$100 x = 100 \times 0.3444... = 34.44...$

Subtract:

$\underline{10 x = ; ; 3.444...}$

$x = \frac{31}{90}$

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Question

If Johnny buys two comic books, priced at $1.50 each, and a candy bar, priced at $0.75, he'll have three quarters and two dimes left over. How much money does he have right now?

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Answer

Add what he can purchase to what he has left over:

Two comic books and the candy bar: $1.50 + $1.0 + $0.75 = $3.75

Three quarters and two dimes: $0.75 + $0.20 = $0.95

Therefore his total amount of money is $3.75 + $0.95 = $4.70.

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Question

Above is the menu at a coffee shop.

Delia has a coupon that entitles her to a free butter croissant with the purchase of one large drink of any kind. The coupon says "limit one per coupon".

She decides to purchase two small espressos, two small cappucinos, and four butter croissants. Disregarding tax, how much will Delia spend?

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Answer

Delia will not use the coupon, since all four of her drinks are small. She will pay full price for:

Two small espressos: $$2.29 \times 2 = $4.58$

Two small cappucinos: $$2.99 \times 2 = $5.98$

Four butter croissants: $$2.29 \times 4 = $9.16$

The total price:

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Question

Find the sum.

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Answer

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Question

Find the sum.

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Question

Convert 0.0004640 into scientific notation.

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Answer

When written in scientific notation, a number will follow the format in which is between one and ten and is an integer value.

To find , take the first non-zero digit in your given number as the ones place. In 0.0004640 this would be the first 4. All subsequent digits fall into the tenths, hundredths, etc. places.

To find , we must count the number of places that is removed. In 0.0004640, the first digit of is in the ten-thousandths place. This indicates that will be .

Together, the final scientific notation will be $4.640*10^{-4}$ .

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Question

Express 770,000,000,000 in scientific notation.

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Answer

Write the number with a decimal point and without commas:

Counting the number of places, move the decimal point to the left until it is after the first nonzero digit:

The resulting number is 7.7; the number of places the decimal point moved to the left was 11. In scientific notation, this number is $7.7 \times 10^{11}$ .

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Question

At the store, green fabric costs $4.53 a yard. How much does 3.8 yards of green fabric cost? (Round to two decimal places.)

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Answer

This is a simple multiplication problem involving decimals. Simply multiply 4.53 by 3.8:

$\small 4.53*3.8 = 17.214$

Now, round to the nearest two decimal places, giving an answer of 17.21.

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Question

Convert into scientific notation.

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Answer

To convert a number into scientific notation, the decimal must be moved until our base number is greater than 1 and less than 10. Next, we must count the number of places we moved it and multiply it by 10 to that number. Thus, our answer is:

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Question

Represent $\small 0.000003452$ in scientific notation.

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Answer

$\small \small \small \small 0.000003452 = 3.452 \times 10^{-6}$

Trick: Count how many times you move the decimal to get 3.452. We moved the decimal 6 times to the right so the exponent above 10 will be -6. If we move the decimal to the left then our exponent would be positive.

Another way to remember whether the exponent will be negative or possitive is whether or not the original number is less than or greater than one. If the original number is less than one, when you put it in scientific notation the exponent above the 10 will be negative. On the other hand, if the original number is greater than one, then the exponent above the 10 will be positive.

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Question

12 grams of oxygen are equal to $6.022 \times 10^{23}$ atoms. Which of the following comes closest to the mass, in grams, of one million atoms of oxygen?

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Answer

In scientific notation, one million atoms is equal to $1 \times 10^{6}$ atoms. To find the mass of this many atoms, we can solve the proportion statement

$\frac{m}{1 \times 10^{6}} = \frac{12} {6.022 \times 10^{23}}$

$m= \frac{12} {6.022 \cdot 10^{23}} \cdot \left (1 \times 10^{6} \right )$

$m= \frac{12 \cdot 10^{6}} {6.022 \cdot 10^{23}}$

$m= \frac{12} {6.022} \cdot \frac{10^{6}}{10^{23}} \approx 1.99 \times 10 ^{-17}$

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Question

Define an operation $\bigstar$ as follows:

For all real numbers ,

$a\bigstar b=a - b + 0.00000001$

Which of the following is equal to $0.00005 \bigstar 0.0000006$ ?

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Answer

Substitute and execute the operations:

$a\bigstar b=a - b + 0.00000001$

$0.00005 \bigstar 0.0000006 = 0.00005 - 0.0000006 + 0.00000001$

Move the decimal point right five places to get it after the first nonzero digit; the scientific notation equivalent is

$4.941 \times 10 ^{-5}$

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