Decimal Operations - PSAT Math

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:

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.

In scientific notation, one million atoms is equal to atoms. To find the mass of this many atoms, we can solve the proportion statement

Substitute and execute the operations:

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

Substitute and execute the operations:

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

Substitute and execute the operations:

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

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

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

Two small espressos:

Two small cappucinos:

Four butter croissants:

The total price:

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

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

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 .

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.

In order to convert the decimal to scientific notation, count the number of spaces from the decimal point to the space between the 4 and the 6 (scientific notation requires that the leftmost number be a number between 1 and 10). In this instance it is 3 spaces. Since the decimal point will be moving from left to right, we know that our exponent will be negative, and in this case -3.

then becomes X .

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

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.

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.

Adding all the charges together and dividing by 2 yields $91.40. Dividing this by 4 yields a monthly installment of $22.85.

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

The reciprocal of this can be found by switching the numerator and the denominator. This is .