Question

1. convert 50 decimeters/week to kilometers/year

26 kilometers/year .026 kilometers/year
.26 kilometers/year 2.6 kilometers/year

1. convert 70,000 quarts/year to pints/day

383.6 pints/day 767.1 pints/day
1,534.2 pints/day 191.8 pints/day

1. convert 700 centiliters/day to liters/year

255.5 liters/year 2,555 liters/year
25.55 liters/year 2.555 liters/year

1. 32,190 inches/year to yards/day

2.4 yards/day 4.9 yards/day
7.3 yards/day 88.19 yards/day

Explanation:

Question 3

Step1: Convert decimeters to kilometers

We know that \(1\) kilometer \( = 10000\) decimeters (since \(1\) meter \( = 10\) decimeters and \(1\) kilometer \( = 1000\) meters, so \(10\times1000 = 10000\) decimeters in a kilometer). So to convert decimeters to kilometers, we divide by \(10000\). Also, there are \(52\) weeks in a year (approximate).

First, convert \(50\) decimeters/week to kilometers/week: \(50\) decimeters \(=\frac{50}{10000}\) kilometers \( = 0.005\) kilometers/week.

Step2: Convert weeks to year

Now, multiply by the number of weeks in a year (\(52\) weeks/year) to get kilometers/year: \(0.005\times52 = 0.26\) kilometers/year? Wait, no, wait. Wait, \(50\) decimeters per week. Let's re - do:

\(1\) decimeter \(= 0.0001\) kilometers (because \(1\) km \( = 10000\) dm, so \(1\) dm \(=\frac{1}{10000}\) km \( = 0.0001\) km). So \(50\) dm/week \(=50\times0.0001\) km/week \( = 0.005\) km/week.

Number of weeks in a year: approximately \(52\). So \(0.005\) km/week \(\times52\) weeks/year \(= 0.26\) km/year? Wait, but let's check again. Wait, maybe I made a mistake in the number of weeks. Wait, actually, the more accurate number of weeks in a year is \(52.1429\) (since \(365\div7\approx52.1429\)). Let's use \(52.1429\) for more accuracy.

So \(50\) dm/week \(= 50\times0.0001\) km/week \( = 0.005\) km/week.

Multiply by \(52.1429\) weeks/year: \(0.005\times52.1429\approx0.2607\) km/year, which is approximately \(0.26\) kilometers/year. Wait, but the options have \(2.6\) as well. Wait, maybe I messed up the conversion factor. Wait, \(1\) decimeter \( = 0.0001\) kilometers? No, \(1\) meter \( = 10\) decimeters, \(1\) kilometer \( = 1000\) meters, so \(1\) kilometer \( = 10\times1000=10000\) decimeters. So \(1\) decimeter \(=\frac{1}{10000}\) kilometers \( = 0.0001\) kilometers. So \(50\) decimeters \( = 50\times0.0001 = 0.005\) kilometers per week.

Number of weeks in a year: \(365\div7\approx52.14\). So \(0.005\times52.14 = 0.2607\approx0.26\)? But the option is \(2.6\). Wait, maybe I made a mistake in the decimal places. Wait, \(50\) decimeters is \(5\) meters (since \(1\) meter \( = 10\) decimeters), \(5\) meters \( = 0.005\) kilometers. Then per week, \(0.005\) km/week. Multiply by \(52\) weeks: \(0.005\times52 = 0.26\) km/year? But the option is \(2.6\). Wait, maybe the number of weeks is taken as \(52\), but maybe I messed up the decimeter - kilometer conversion. Wait, \(1\) decimeter \( = 0.0001\) kilometers, so \(50\) decimeters \( = 0.005\) kilometers per week. \(0.005\times52 = 0.26\), but the option is \(2.6\). Wait, maybe I flipped the conversion. Wait, \(1\) kilometer \( = 10000\) decimeters, so \(1\) decimeter \( = 1e - 4\) kilometers. So \(50\) decimeters \( = 50\times1e - 4=0.005\) km/week. Multiply by \(52\) weeks: \(0.005\times52 = 0.26\) km/year. But the option is \(2.6\). Wait, maybe the question assumes \(52\) weeks, but maybe I made a mistake. Wait, another way: \(50\) decimeters per week. \(50\) decimeters \( = 5\) meters. \(5\) meters per week. In a year (52 weeks), that's \(5\times52 = 260\) meters per year. \(260\) meters \( = 0.26\) kilometers per year. Ah! Yes, because \(1\) kilometer \( = 1000\) meters, so \(260\) meters \(=\frac{260}{1000}=0.26\) kilometers per year. So the answer is \(0.26\) kilometers/year.

Step1: Convert quarts to pints

We know that \(1\) quart \( = 2\) pints. So to convert quarts/year to pints/year, we multiply by \(2\). So \(70000\) quarts/year \(=70000\times2\) pints/year \( = 140000\) pints/year.

Step2: Convert year to day

There are \(365\) days in a year. So to convert pints/year to pints/day, we divide by \(365\). So \(\frac{140000}{365}\approx383.56\) pints/day, which is approximately \(383.6\) pints/day.

Step1: Convert centiliters to liters

We know that \(1\) liter \( = 100\) centiliters. So to convert centiliters to liters, we divide by \(100\). So \(700\) centiliters/day \(=\frac{700}{100}\) liters/day \( = 7\) liters/day.

Step2: Convert day to year

There are \(365\) days in a year. So to convert liters/day to liters/year, we multiply by \(365\). So \(7\) liters/day \(\times365\) days/year \( = 2555\) liters/year? Wait, no, wait: \(700\) centiliters/day. \(700\) centiliters \( = 7\) liters (since \(1\) L \( = 100\) cL). Then per day \(7\) liters. In a year (365 days), \(7\times365 = 2555\) liters/year? But the options are \(255.5\), \(2555\), \(25.55\), \(2.555\). Wait, I must have made a mistake. Wait, \(700\) centiliters/day. \(1\) liter \( = 100\) centiliters, so \(700\) centiliters \( = 7\) liters? No, \(700\) centiliters \(=\frac{700}{100}=7\) liters? Wait, no, \(1\) liter is \(100\) centiliters, so \(700\) centiliters is \(7\) liters? But that can't be right. Wait, no, \(1\) centiliter is \(0.01\) liters, so \(700\) centiliters \( = 700\times0.01=7\) liters. Then per day \(7\) liters. In a year, \(7\times365 = 2555\) liters/year. But the option is \(2555\) liters/year? Wait, the options are \(255.5\), \(2555\), \(25.55\), \(2.555\). Wait, maybe I messed up the conversion. Wait, \(700\) centiliters/day. Let's do it step by step:

\(700\) centiliters \( = 7\) liters? No, wait, \(1\) liter \( = 100\) centiliters, so \(700\) centiliters \(=\frac{700}{100} = 7\) liters? But that seems high. Wait, no, maybe the question is using \(365\) days, but maybe I made a mistake. Wait, no, \(700\) centiliters per day. \(700\) cL/day \( = 7\) L/day. \(7\) L/day \(\times365\) days/year \( = 2555\) L/year. So the answer is \(2555\) liters/year.

Answer:

\(\boldsymbol{0.26}\) kilometers/year (the option with \(.26\) kilometers/year)

Question 4