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There is no need to add zeros to the end of either number here because they both have the same number of decimal places. Ignore the decimal point for the moment and continue adding as usual. Then, finally, add the decimal point to the sum. The sum of the decimals is $10.10,$ or just $10.1.$ This means that Zosia's video is $10.1$ minutes long. Notice that the numbers do not have the same number of decimal places. To make the subtraction easier, add one zero to the end of the first number so that both numbers have an equal number of decimal places. Now ignore the decimal points and continue subtracting as usual, then place the decimal point in the difference. The difference of the decimals is $8.83.$ This means that the final length of the video is $8.83$ minutes.

Each factor will be rounded to the greatest place value to estimate this product. In the number $59,$ the digit with the greatest place value is $5.$ In the other factor, the digit with the greatest place value is $1.$ Now, take a look at the digit to the right of the greatest place value.

• If the digit is less than $5,$ the underlined number remains the same.
• If the digit is $5$ or greater, add $1$ to the underlined number.

After that, make all digits to the right of the greatest place value zero. Starting with the first factor, the digit to the right of the underlined number is $9.$ This is greater than $5,$ so the digit in the rounded place is increased by $1$ and the other digit is changed to a $0.$ For $1.75,$ the number in the tenths place is $7.$ Since $7$ is greater than $5,$ the number in the rounded place $1$ is increased by $1$ and the other digits are converted to $0.$ In this case, the zeros can be ignored because they will not change the value of the product. The product of $60$ and $2$ is $120.$ Mark will pay about $120$ dollars. The steps for multiplying these numbers is the same as multiplying two decimal numbers.

1. Multiply the numbers as if the decimal factor were a whole number.
2. Count the number of decimal places in the decimal factor.
3. The number of decimal places in the product is the same as the number of decimal places in the decimal factor.

Start by multiplying $59$ and $175.$ The product of the numbers is $10325.$ Since there are two decimal places in $1.75,$ the product of $59$ and $1.75$ must be a decimal number with two decimal places. The product is $103.25.$ This means that Mark will pay Zosia $103.25$ dollars.

The digit to the right of the greatest place value determines how the number is rounded.

• If the digit is less than $5,$ the number in the rounded place remains the same.
• If the digit is $5$ or greater, add $1$ to the number in the rounded place.

After rounding, remove any decimal digits and convert the non-decimal digits to the right of the greatest place value into $0.$ Since the digit with the greatest place value is the leftmost non-zero digit int he number, $103.25$ has its greatest place value in the hundreds place and $0.113$ in the tenths place. In $103.25,$ the digit in the tens place is $0.$ Since $0$ is less than $5,$ the digit in the hundreds place $1$ remains the same and the other digits are replaced with $0.$ This results in the estimated number $100.$ In $0.113,$ the number in the hundredths place is $1.$ Since $1$ is less than $5,$ the number in the tenth place $1$ is kept unchanged. Then, the other digits are replaced with $0.$ Since these zeros do not change the value of the number, they can be omitted. Multiplying a number by $0.1$ means dividing the number by $10$ because $0.1=\frac{1}{10}.$ This means that the product of $100$ and $0.1$ is $10.$ The platform pays about $\$10$ for $59$ views.

1. Multiply as if the factors were whole numbers.
2. Count the number of decimal places in each factor.
3. The number of decimal places in the product is the sum of the number of decimal places in each factor.

Start by multiplying $10325$ and $113.$ There are $2$ decimal places in the first factor $103.25,$ and there are $3$ decimal places $0.113.$ This means that the product of the decimal numbers must be a decimal number with $2+3=5$ decimal places. The product of the numbers is $11.66725.$ Since money is represented by numbers with two decimal places, $11.66275$ is rounded to two decimal places. The platform pays $11.67$ dollars for $59$ views. This is close the estimate found in Part A, so this answer is reasonable.

Since the area of a square is the product of its two sides, this square has an area of $0.1\times 0.1$ square units. Now multiply the decimals as if they were whole numbers. Then, count the number of decimal places in each factor and add them. The number of decimal places in the product must be $2.$ Insert zeros to the left of $1$ and move the decimal point two places to the left. The area of a single square is $0.01$ square unit.

In the previous part, it is found that the area of a each square is $0.01.$

Since there are $6$ small squares, the area of the rectangle can be found by multiplying $0.01$ by $6.$ Multiply the numbers as if they were whole numbers. The sum of the number of decimal places in each factor is $2.$ This means that the number of decimal places in the product must be $2.$ The area of the rectangle is $0.06.$ This is also equal to the product of $0.2$ and $0.3.$ Alternatively, the Commutative and Associative Properties of Multiplication can be used to find the product. Either way, the answer is the same!