Question

place value relationships within whole numbers and decimals - item 94273
question 2 of 5
yasir says that this picture represents 3.4.
giselle says that this picture represents 34.
use the drop - down menus to explain how either could be correct.
yasir is correct if each blue rectangle represents
and each green square represents
.
giselle is correct if each blue rectangle represents
and each green square represents
.
in yasirs model, each piece represents a value that is
the value it represents in giselles model.

Explanation:

Step1: Analyze Yasir's claim (3.4)

There are 3 blue - rectangles and 4 green - squares. If the number is 3.4, assume each blue rectangle represents 1 and each green square represents 0.1. Then \(3\times1 + 4\times0.1=3 + 0.4 = 3.4\).

Step2: Analyze Giselle's claim (34)

If the number is 34, assume each blue rectangle represents 10 and each green square represents 1. Then \(3\times10+4\times1 = 30 + 4=34\).

Step3: Find the ratio of values

The value of a blue - rectangle in Yasir's model is 1 and in Giselle's model is 10. The value of a green - square in Yasir's model is 0.1 and in Giselle's model is 1. So each piece in Yasir's model represents a value that is \(\frac{1}{10}\) of the value it represents in Giselle's model.

Answer:

Yasir is correct if each blue rectangle represents 1 and each green square represents 0.1.
Giselle is correct if each blue rectangle represents 10 and each green square represents 1.
In Yasir's model, each piece represents a value that is \(\frac{1}{10}\) the value it represents in Giselle's model.