Division with decimal quotients

Learning Objectives Calculate the scale factor between two similar figures when the ratio results in a decimal. Determine if two figures are similar by dividing corresponding side lengths to find a consistent decimal ratio. Use long division to find a decimal quotient to a specified number of decimal places. Solve for an unknown side length in a similar figure, resulting in a decimal answer. Interpret a decimal quotient as a scale factor of enlargement (k > 1) or reduction (0 < k < 1). Accurately place the decimal point in the quotient when dividing integers. Apply division with decimal quotients to solve real-world problems involving scale models and maps. Ever tried to resize a picture and it ended up stretched and weird? 🖼️ To keep the shape perfect, every part...

TermDefinitionExample Decimal QuotientThe result of a division problem that includes a decimal point. This occurs when the divisor does not divide the dividend into a whole number.10 ÷ 4 = 2.5. The decimal quotient is 2.5. SimilarityTwo geometric figures are similar if they have the exact same shape but can be different sizes. Their corresponding angles are equal, and the ratio of their corresponding side lengths is constant.A 3-4-5 right triangle is similar to a 6-8-10 right triangle because all sides of the second triangle are twice the length of the sides of the first. Corresponding SidesSides that are in the same relative position in two similar figures.In two similar rectangles ABCD and WXYZ, side AB corresponds to side WX. Scale Factor (k)The constant ratio used to enlarge or reduce...

Scale Factor Formula k = \frac{\text{Image Side Length}}{\text{Pre-image Side Length}} To find the scale factor (k) that transforms a pre-image into an image, divide the length of a side on the image by the length of the corresponding side on the pre-image. The result is often a decimal. Decimal Placement in Long Division Dividend ÷ Divisor = Quotient To perform division that results in a decimal, place a decimal point after the last digit of the dividend and add trailing zeros. The decimal point in the quotient goes directly above the decimal point in the dividend. Proportionality in Similar Figures \frac{A'B'}{AB} = \frac{B'C'}{BC} = \frac{C'A'}{CA} = k For two similar triangles ABC and A'B'C', the ratio of any pair of c...