Which explains the number of decimal places in the product 0.42 x 3.8 x 10.51?

a. the greatest number of decimal places in any of the factors is 1. so, the product will have 1 decimal place.

b. the greatest number of decimal places in any of the factors is 2. so, the product will have 2 decimal places.

c. there are a total of 4 decimal places in the factors. so, the product will have 4 decimal places.

d. there are a total of 5 decimal places in the factors. so, the product will have 5 decimal places.

  D. There are a total of 5 decimal places in the factors. So, the product will have 5 decimal places

Step-by-step explanation:

If you were to convert these factors to integers with a multiplier of 10 to some power, they would be ...

  (42×10⁻²) × (38×10⁻¹) × (1051×10⁻²)

Each of the exponents of 10 is the opposite of the number of decimal places the number had.

The product would be the product of the integers with a multiplier of 10 to the total of the powers. That total is the opposite of the total number of decimal digits in the factors.

  = 1677396×10⁻⁵

Converted back to standard form, the decimal point is placed so there are 5 decimal digits:

  = 16.77396

This is basically the method we're taught to use for decimal multiplication: multiply as though the numbers were integers, and place the decimal point so the total number of decimal digits in the product is equal to the total number of decimal digits in the factors. (Beware products that end in 0. Those zeros are significant when you're counting decimal places.)

  Example: 0.25 × 0.4 = 0.100 . . . . . 2+1 = 3 decimal places

Please note that this is a description of how you do multiplication of numbers with decimal fractions. It is not a description of how you appropriately deal with measurement values assumed to have some associated error. The numbers here are presumed exact. A different set of rules applies to choosing an appropriate number of significant digits when measurements or estimates are involved.

b. astronomers

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.