\(0.1+0.1+0.1=0.3\)

So, \(3\times0.1=0.3\)

The mass is 0.3 kilograms.

asked 2021-08-02

Ben and Carl are remembering how you told them that a 0 at the end of a whole number makes it ten times greater. They remember that 420 is ten times bigger than 42, for example. They wonder if the same thing works with decimals. Ben argues that putting a 0 at the end of a decimal number makes it ten times greater. Carl says, "No. You've gotta sneak it in right after the decimal point and push everything to the right." How do you help them to see what's true and what's not?

asked 2021-08-08

When multiplying decimals, how do you know where to place the decimal point? Think about this as you do parts (a) through (d) below.

a. Write two equations for multiplying 0.3 by 0.16. One equation should express the factors and product using decimals, and one using fractions.

b. In part (a), you multiplied tenths by hundredths to get thousandths. Do you always get thousandths if you multiply tenths by hundredths? Why or why not? What do you get if you multiply tenths by tenths? Hundredths by hundredths? Use several examples to justify your answers.

c. When a multiplication problem is written using decimals, there is a relationship between the number of decimal places in the parts (or factors) of the problem and the number of decimal places in the answer (or product). Describe this relationship.

d. Describe a shortcut for locating the decimal point in the answer to a problem involving decimal multiplication.

a. Write two equations for multiplying 0.3 by 0.16. One equation should express the factors and product using decimals, and one using fractions.

b. In part (a), you multiplied tenths by hundredths to get thousandths. Do you always get thousandths if you multiply tenths by hundredths? Why or why not? What do you get if you multiply tenths by tenths? Hundredths by hundredths? Use several examples to justify your answers.

c. When a multiplication problem is written using decimals, there is a relationship between the number of decimal places in the parts (or factors) of the problem and the number of decimal places in the answer (or product). Describe this relationship.

d. Describe a shortcut for locating the decimal point in the answer to a problem involving decimal multiplication.

asked 2021-06-08

Show that the decimals 0.6, 0.1, 0.2, and 0.325 are positive rational numbers.

asked 2021-05-02

The owner of a pet food store wants to mix birdseed that costs $1.25 per pound with sunflower seeds that cost $0.75 pe pound to make 50 pounds of a mixture that costs $1.00 per pound. How many pounds of each type of seed should he use?

asked 2021-06-12

The decimals chart in this lesson shows that we line up the decimal points when we add or subtract decimal numbers. Why do we do that?

asked 2021-08-03

Solve Equations with Decimal Coefficients In the following exercises, solve the equation by clearing the decimals.

\(\displaystyle{0.05}{n}+{0.10}{\left({n}+{7}\right)}={3.55}\)

\(\displaystyle{0.05}{n}+{0.10}{\left({n}+{7}\right)}={3.55}\)

asked 2021-06-03

To clear the decimals in an equation, how do you determine what power of 10 to multiply each side of the equation by?