Decimals - ACT Math

To add decimals, first add zeros to the necessary terms so they all have the same number of places to the right of the decimal point.

Now, temporarily drop the decimal and add the numbers as if they were whole numbers.

Finally, add the decimal place back in, in the same place you removed it from. In this case, we originally modified our numbers so they all had 3 numbers to the right of the decimal, so we will add the decimal back to the exact same place. Thus, our answer is:

Rewrite the problem so that the tenths, hundredths, and thousandths digits align. Use zeros as placeholders and solve.

To determine this answer, move the decimal point in 3.0147 until you get 3,014,700,000 (9 places). There are 9 decimal places after the decimal point.

We want to move the decimal point to the place just after the first non-zero number, in this case 6, and then drop all of the non-significant zeros. We need to move the decimal point five spaces to the right, so our exponent should be negative. If the decimal had moved left, we would have had a positive exponent.

In this case we get 6.009 * 10–5.

Slide the decimal point to the left as many places as you need to make a number between 1 and 10. Multiply that number by 10 to the power of however many decimal places you moved the decimal.

450,000 = 4.5 x 100,000

100,000 = 105 (exponent is equal to the number of zeros)

450,000 = 4.5 x 105

We need to convert into a number of the form .

The trick is, however, figuring out what should be. When you have to move your decimal point to the right, you need to make the decimal negative. (Note, though, when you multiply by a negative decimal, you move to the left. We are thinking in "reverse" because we are converting.)

Therefore, for our value, . So, our value is:

The easiest way to do this is to convert each of your answer choices into scientific notion and compare it to .

For each of the answer choices, this would give us:

(Which is, thus, the answer.)

When you convert, you add for each place that you move to the left and subtract for each place you move to the right. (Note that this is opposite of what you do when you multiply out the answer. We are thinking in "reverse" because we are converting.)

This is a bit of a scientific notation application test.

Because is in the ones place , , and because is in the hundredths place , .

From there, it becomes self-explanatory:

.

Remember to take care that you do not give or instead of .

0.625 is equal to , while .25 is equal to . Dividing by fractions is the same as multiplying by the reciprocal of the divisor. Thus, which equals , which simplifies to 2.5.

Eliminate the decimal place on the denominator by moving the decimal place 2 spaces to the right. Follow suit for the numerator. The decimal place should also move the same number of units to the right. Evaluate.

Rewrite so that both are in fraction form.

Convert the division sign to multiplication, and take the reciprocal of the 2nd term.

Begin by multiplying all of your decimal fractions by :

Simplify:

Now perform the multiplication:

The easiest thing to do next is to subtract from :

Next, convert into the fraction :

Now, the common denominator can be :

Simplify:

0.825 in fraction form is . Simplifying the fraction equals .

1. Convert all of your decimal fractions to normal fractions by multiplying each by :

2. Find the least common denominator for all of the fractions and use that denominator:

In this case it's 7 x 9 x 10 = 630

3. Add together all of the fractions you now have:

4. Simplify this fraction into a mixed number:

1. Multiply the two fractions together in decimal form:

2. Multiply the new fraction by 10,000/10,000:

3. Simplify this fraction using the greatest common factor:

In this case the GCF is 15: