RESULT You must line up the decimals because when you add or subtract numbers you must do so according to their place value.

asked 2021-06-19

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 2021-09-09

(i) How close to 4 do we need to take x so that \(\displaystyle{\left(\frac{{x}}{{2}}-{2}\right)}{<}{0.001}\) ?

(ii) How close to 4 do we need to take x so that \(\displaystyle{\left(\frac{{x}}{{2}}-{2}\right)}{>}{0.0001}\) ?

(iii) How close to 0 do we need to take x so that \(\displaystyle{\left({2}{x}+{9}\right)}{<}{9.0001}\) ?

(iv) How close to 0 do we need to take x so that \(\displaystyle{\left({2}{x}+{9}\right)}{>}{8.999}\)?

(v) How close to 0 do we need to take x so that \(\displaystyle{\left({x}^{{{2}}}+{6}{x}+{9}\right)}{<}{9.001}\) ?

(vi) How close to 0 do we need to take x so that \(\displaystyle{\left({x}^{{{2}}}+{6}{x}+{9}\right)}{<}{9.0001}\) ?

(vii) How close to 0 do we need to take x so that \(\displaystyle{\left({x}^{{{2}}}+{6}{x}+{9}\right)}{>}{8.9999}\) ?

(viii) How close to -7 do we need to take x so that \(\displaystyle\frac{{1}}{{\left({x}+{7}\right)}^{{{4}}}}{>}{10000}\) ?

(ix) How close to −7 do we need to take x so that \(\displaystyle\frac{{1}}{{\left({x}+{7}\right)}^{{4}}}{>}{100000}\) ?

(x) How close to 0 do we need to take x so that \(\displaystyle{\ln{{x}}}{<}-{10000}\)?

(b) Use the definition of a limit to show that

(i) \(\displaystyle\lim{x}\rightarrow{4}\)

\(\displaystyle{\left(\frac{{x}}{{2}}-{2}\right)}={0}\)

(ii) \(\displaystyle\lim{x}\rightarrow{0}\)

\(\displaystyle{\left({2}{x}+{9}\right)}={9}\)

(iii) \(\displaystyle\lim{x}\rightarrow{0}\)

\(\displaystyle{\left({x}^{{{2}}}+{6}{x}+{9}\right)}={9}\)

(iv) \(\displaystyle\lim{x}\rightarrow-{7}\)

\(\displaystyle\frac{{1}}{{\left({x}+{7}\right)}^{{{4}}}}=\infty\)

(v) \(\displaystyle\lim{x}\rightarrow{0}+\)

\(\displaystyle{\ln{{x}}}=-\infty\)

asked 2021-08-22

In the following exercises, add or subtract.

Given: \(\displaystyle-{4.2}+{\left(-{9.3}\right)}\)

Given: \(\displaystyle-{4.2}+{\left(-{9.3}\right)}\)

asked 2021-05-08

asked 2021-06-10

The given question is \(93.6-0.518\)

That means we have to subtract the number 0.158 from the number 93.6.

That means we have to subtract the number 0.158 from the number 93.6.

asked 2021-08-03

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

\(\displaystyle{0.4}{y}-{4}={2}\)

\(\displaystyle{0.4}{y}-{4}={2}\)