A thousandths grid is completely coloured in when tree different decimals are shown. One decimal is double of the others.
To understand this problem, let's break it down step by step.
Step 1: Understand what a thousandths grid is.
A thousandths grid is a representation of numbers from 0 to 1, divided into 1,000 equal parts or squares. Each square represents 0.001 (one thousandth).
Step 2: Understand the statement "completely colored in."
When a thousandths grid is completely colored in, it means that squares representing a decimal or fraction are shaded or filled.
Step 3: Identify the three decimals.
Let's assume the three decimals are represented as decimal A, decimal B, and decimal C.
Step 4: Determine the relationship between the three decimals.
According to the problem, one decimal is double the others. Let's suppose decimal A is double decimal B and decimal C. This means that decimal A = 2 * decimal B = 2 * decimal C.
Step 5: Determine the coloring condition.
To completely color in the thousandths grid, we need to find three decimals that, when multiplied by 1,000, will give us whole numbers. These whole numbers will be used to color the corresponding number of squares.
Step 6: Solve the problem.
Since one decimal is double the others, we can express decimal A as 2x (where x represents the other decimals, i.e., decimal B and decimal C). We can set up an equation: 2x + x + x = 1 (since the grid represents 1 whole). Simplifying the equation, we get 4x = 1. Dividing both sides by 4, we find that x = 1/4.
Therefore, decimal A = 2 * (1/4) = 1/2
decimal B = 1/4
decimal C = 1/4
To color in the thousandths grid completely, we would shade or fill:
For decimal A, we would shade 500 squares (since 0.5 * 1000 = 500).
For decimal B and decimal C, we would shade 250 squares each (since 0.25 * 1000 = 250).
So, the problem is solved by finding the relationship between the decimals and using the appropriate multiplication factor to determine the number of squares to shade or fill in the thousandths grid.